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TOPOLOGY (see E, 285). Lacan makes repeated reference to FechnerThe term '[[topology]]''s expres-

sion in his work (eThe [[representation]] on a map of the physical features of a landscape.g In [[psychoanalysis]] the term is used to describe the differentiation of the mind or [[psyche]] into subsystems with specific functions and characteristics. E [[Freud]]'s topographies of the [[psyche]] owe much to nineteenth-century theories of cerebral localization, 193); which ascribe different mental functions to different areas of the brain. It was the study of [[dream]]s that led [[Freud]] to the conclusion that [[unconscious]] activities such as dreaming are quite divorced from the [[conscious]] mind and literally take place on 'other scene' is, in Lacanian terms, the Otherein anderer Schauplatz'' (another stage or theatre).

theatre in which the subject plays out hiS FANTASYThe first, which is built on the edificeelaborated between 1900 and 1915, describes an apparatus comrpising [[unconscious]], [[preconscious]] and [[conscious]] systems, with mechanism of [[censorship]] to prevent ideas from moving between them.

Considerations of representability and other mechanisms of the real ([[dream-work]] filter or censor the world). The scene content of fantasy [[dream]]s and [[fantasies]] before allowing them to enter the [[conscious]] mind, usually because their sexual content is a virtual space which is framed,unacceptable to [[conscious]] thought-processes.

in The second or '[[structural]]' [[topography]], elaborated from 1920 onwards, describes a [[structure]] of three agencies known respectively as the same way that [[id]], the scene of a play is framed by [[ego]] and the proscenium arch in a[[super-ego]].

1962-3: seminar [[Topology]] refers primarily to the branch of 19 December 1962)[[mathematics]] that rigorously treats questions of neighborhoods, limits, and continuity. The notion of scene is used by Lacan

[[Psychoanalysts]] have applied it to distinguish between ACTING OUT and PASSAGE TO THE ACTthe study of [[unconscious]] [[structure]]s. The former still

remains inside [[Topology]] (''topologie'') is a branch of [[mathematics]] which deals with the sceneproperties of figures in space which are preserved under all continuous deformations. These properties are those of continuity, for it contiguity and delimitation. The notion of space in topology is still inscribed in one of topological space, which is not limited to Euclidean (two- and three-dimensional space), nor even to spaces which can be said to have a dimension at all.  Topological space thus dispenses with all references to distance, size, area and angle, and is based only on a concept of closeness or neighbourhood. ==Freud==In what have been called his two "topographies" (the first dating from 1900 and the second from 1923), [[Freud]] resorted to [[schema]]s to represent the various parts of the symbolic order[[psychic apparatus]] and their interrelations. The

passage to the act, however, is These schemas implicitly posited an exit from the scene, is a crossing over fromequivalence between [[psychic space]] and [[Euclidean space]].

Freud used spatial metaphors to describe the symbolic to psyche in ''[[The Interpretation of Dreams]]'', where he cites G. T. Fechner's idea that the real; there scene of action of dreams is a total identification with different from that of waking ideational life and proposes the object (objetconcept of 'psychical locality'.

petit Freud is careful to explain that this concept is a)purely topographical one, and hence an abolition of the subject (Lacanmust not be confused with physical locality in any anatomical fashion.<ref>Freud, 1962-31900a: seminar of 16SE V, 536</ref>

January 1963His 'first topography' divided the psyche into three systems: the conscious (Cs), the [[preconscious]] (Pcs) and the [[unconscious]] (Ucs). The fantasy scene is also an important aspect in PERVERSION.

The pervert typically stages his enjoyment in terms 'second topography' divided the psyche into the three agencies of some highly stylisedthe [[ego]], the [[superego]] and the [[id]].

scene==Lacan==Early on, and according [[Jacques Lacan]] noted that the limitations of such a naive topology had restricted [[Freudian theory]], not only in the description of the [[psychic apparatus]] (a description that in the end required an appeal to a stereotypical scriptthe economic point of view), but also in the specificity of [[clinical structure]]s.

The [[representation]] on a map of the physical features of a landscape.In [[psychoanalysis]] the term is used to describe the differentiation of the mind or psyche into subsystems with specific functions and characteristicsBut already he saw them as more than just models.

With the [[FreudBorromean knot]]'s topographies of the psyche owe much to nineteenth-century theories of cerebral localization, which ascribe different mental functions to different areas of introduced in 1973, he took the brain.IT was the study position that these [[object]]s were a real presentation of dreams that led Freud to the conclusion that unconscious activities such as dreaming are quite divorced from the conscious mind [[subject]] and literally take place on ''ein anderer Schauplatz'' (another stage or theatre)not just a [[representation]].

[[Freud]] evolved two distinct topographies.The first, elaborated between 1900 and 1915, describes an apparatus comrpising [[unconscious]], [[preconscious]] and [[conscious]] systems, with mechanism Below are several of [[censorshipLacan]] to prevent ideas from moving between them.Considerations of representability and other mechanisms of the [[dream-work]] filter or censor the content of dreams and fantasies before allowing them to enter the [[conscious]] mind, usually because their sexual content is unacceptable to conscious thought-processes.The second or 'structural' topography, elaborated from 1920 onwards, describes a structure of trhree agencies known respectively as the [[id]], the s [[egotopology|topological]] and the [[super-egoobject]]s.

[[Topology]] refers primarily to Lacan formalized this property in the branch of [[mathematics]] that rigorously treats questions of neighborhoodsdouble loop, limitsor "interior eight, and continuity" in which the gap created by the cut is closed after a second trip around a fictional axis.

[[Psychoanalysts]] have applied it to The difference of the study of [[unconscious]] [[structure]]ssignifier from itself is indicated by the difference between the two trips around the loop (Figure 1).

[[Topology]] (''topologie'') is If a branch of [[mathematics]] which deals with signifier represents the properties of figures in space which are preserved under all continuous deformations.These properties are those of continuitysubject for another signifier, contiguity and delimitation. The notion of space in topology is one of topological space, which is not limited to Euclidean (two- and three-dimensional space), nor even to spaces which can then the subject would be said to have supported by a dimension at all. Topological space thus dispenses with all references to distance, size, area and angle, and is based only on surface whose edge would be a concept of closeness or neighbourhoodsignifying cut.

==Freud==In what have been called his two "topographies" (the first dating from 1900 and the second from 1923), [[Freud]] resorted to [[schema]]s to represent the various parts of the [[psychic apparatus]] and their interrelations. These schemas implicitly posited an equivalence between [[psychic space]] and [[Euclidean space]]The double loop cannot be drawn on a plane without showing a cut.

Freud used spatial metaphors to describe the psyche in ''[[The Interpretation of Dreams]]'', where he cites G. T. Fechner's idea that the scene of action of dreams same is different from that of waking ideational life and proposes the concept true of 'psychical locality'. Freud is careful to explain that this concept is a purely topographical onesphere, and must not be confused with physical locality in any anatomical fashion.<ref>Freud, 1900a: SE V, 536</ref> His 'first topography' divided the psyche into three systems: the conscious (Cs), the [[preconscious]] (Pcs) and the [[unconscious]] (Ucs). The 'second topography' divided the psyche into the three agencies a simple representation of the ego, the superego and the iduniverse.

==Lacan==Early The Möbius strip, on, [[Jacques Lacan]] noted that the limitations of such a naive topology had restricted [[Freudian theory]]other hand, not only in can represent this cut and symbolize the description subject of the [[psychic apparatus]] (a description that in the end required an appeal to the economic point of view), but also in the specificity of [[clinical structure]]s.The hypothesis that [[the unconscious is structured like a language,]] that is, in two dimensions, led [[Lacan]] to the [[topology]] of [[surface]]s. The concept of '[[foreclosure]]', for example, which he constructed on the basis of this [[topology]], confirmed the heuristic value of his approach.

In his 1961-1962 seminar "[[L%27identification|Identification]]", [[Lacan]] unveiled Since a collection of [[topology|topological]] [[object]]s — such as the [[torus]], the [[Möbius strip]]only has one surface, and it is possible to pass from one side to the [[cross-cap]] — that served pedagogical aims. But already he saw them as more than just models. With other without crossing over any edge—an apt representation of the ]]Borromean knot\\, introduced in 1973, he took the position that these [[object]]s were a real presentation return of the [[subject]] and not just a [[representation]]repressed.

Below are several of [[Lacan]]'s [[topology|topological]] [[object]]sThe Möbius strip also has certain other peculiarities.

==The Cut A cut that runs one-third from the edge and parallel to the edge divides the strip into a two-sided strip linked to what remains of the Signifier==original Möbius strip.

Far from being given a priori, every space But if this cut is organized on the basis of cuts and can actually be considered as a cut made in the space of a higher dimension. We are familiar with the subjective impact of this: The events of our lives only become history through the castration complexcenter, which organizes our reality at it does not divide the price of an imaginary cutting off of the penis. According to Freud, by introjecting a single trait of another, the subject identifies with the other (at the price of losing this person as a love object). In the single trait Lacan found the very structure of the signifier: A cut allows the lost object to fall away. He called this cut the "unary traitMöbius strip in two."

The linguist Ferdinand de Saussure insisted on the fundamentally negative, purely differential character of the signifier. Lacan formalized this property in the double loopInstead, or "interior eight," in which the gap created by the cut entire strip is closed after a second trip around transformed into a fictional axis. The difference of the signifier from itself is indicated by the difference between the strip with two trips around the loop (Figure 1)sides.

==The This characteristic illustrates the equivalence between the Möbius Strip strip (the subject) and Interpretation==the medial cut that transforms it, and also provides a model of how interpretation functions.

If a signifier represents the subject for another signifier, then the subject would be supported by a surface whose edge would be a signifying cut. Note that the plane—the usual screen for the subject's images, figures, and dreams, that is, plans—is a surface that Interpretation does not meet these conditions. The double loop cannot be drawn on a plane without showing a cut. The same is true of a sphere, a simple representation of abolish the universeunconscious.

The Möbius strip, on the other hand, can represent this cut and symbolize the subject of the unconscious. Since a Möbius strip only has one surface, it is possible to pass from one side to the other without crossing over any edge—an apt representation of the return of the repressed. The Möbius strip also has certain other peculiarities. A cut that runs one-third from the edge and parallel to the edge divides the strip into a two-sided strip linked to what remains of the original Möbius strip. But if this cut is made in the center, it does not divide the Möbius strip in two. Instead, the entire strip is transformed into a strip with two sides. This characteristic illustrates the equivalence between the Möbius strip (the subject) and the medial cut that transforms it, and also provides a model of how interpretation functions. Interpretation does not abolish the unconscious. On the contrary, it makes the unconscious real for the subject by its transformed appearance as another (an Other) surface (figure 2).

Lacan made different uses of the torus.  By drawing Venn diagrams, traditionally used to illustrate basic logical operations, on the surface of the torus, he demonstrated the extent to which our thinking depends upon the plane surface, and he also provided another possible basis for the logic of the unconscious (Figure 3).

On the torus, only symmetrical difference is consistent. Thus we have a demonstration of how the signifier can be different from all other signifiers and also from itself.

Lacan also used the torus to represent the subject as the subject Thus we have a demonstration of demand. In this sense, how the torus signifier can be conceived as the surface created by the iteration of the trajectory of the subject's demand. This trajectory turns around two different empty spaces, one that is "internal," D, the lack created in the real by speech, from all other signifiers and one that is "central," d, corresponding to the place of the elusive object of desire that the drive goes around before completing the loop (Figure 5)also from itself.

Lacan also used the torus to represent the subject as the subject of demand.  In this sense, the torus can be conceived as the surface created by the iteration of the trajectory of the subject's demand.  This trajectory turns around two different empty spaces, one that is "internal," D, the lack created in the real by speech, and one that is "central," d, corresponding to the place of the elusive object of desire that the drive goes around before completing the loop (Figure 5). For every torus, there is a complementary torus, and the empty spaces of the two are the inverse of each other.  Lacan made this structure of complementary toruses the support of the neurotic illusion that makes the demand of the Other the object of subject's desire and, conversely, makes the desire of the Other the object of subject's demand.  This structure also arises from the fact that on a torus, the signifying cut (the double loop) does not detach any fragment.  Neurotic subjects, insofar as they give in to neurosis, insofar as they are "in the torus," are not organized around their own castration, but instead excuse themselves by substituting the Other's demand for the object of their fantasy (figure 6).

The cross-cap, or more precisely, the projective plane, can represent the subject of desire in relation to the lost object.  A double loop drawn on its surface in effect divides this single-sided surface into two heterogeneous parts: a Möbius strip representing the subject and a disk representing object a, the cause of desire.  The disk is centered on a point that is related to the irreducible singularity of this surface, which Lacan identified with the phallus.  Unlike the representation of the subject produced on the torus, here a single cut, which symbolizes castration, produces both the subject and the object in its divisions (figure 7).

Introduced by Lacan in 1973, the Borromean knot is the solution to a problem perceivable only in Lacanian theory but having extremely practical clinical applications.  The problem is: How are the three registers posited as making up subjectivity—the real (R), the symbolic (S), and the imaginary (I)—held together? Indeed, the symbolic (the signifier) and the imaginary (meaning) seem to have hardly anything in common—a fact demonstrated by the abundance and heterogeneity of languages.  Moreover, the real, by definition, escapes the symbolic and the imaginary, since its resistance to them is precisely what makes it real.  This is why Lacan identified the real with the impossible.)

IndeedIn psychoanalysis, the symbolic (the signifier) real resists, and thus is distinct from, the imaginary (meaning) seem defenses that the ego uses specifically to have hardly anything in common—a fact demonstrated by misrecognize the abundance impossible and heterogeneity of languages. Moreover, the real, by definition, escapes the symbolic and the imaginary, since its resistance to them is precisely what makes it realconsequences.