topology ({{Top}}[[topologie) Topology (originally called analysis situs by]]{{Bottom}}
Leibniz) =====Definition====="[[Topology]]" is a branch of [[mathematics ]] which deals with the properties of [[figures]] in [[topology|space]] where are preserved under all continuous deformations. These properties are those of continuity, contiguity and delimitation.
=====Toplogical Space=====The [[notion]] of [[topology|space]] in [[topology]] is one of [[topology|topological space ]], which are preserved under is not limited to Euclidean (two- and [[three]]-dimensional [[space]]), nor even to spaces which can be said to have a [[dimension]] at all continuous deformations. These proper-[[topology|Topological space]] thus dispenses with all references to distance, size, area and angle, and is based only on a [[concept]] of closeness or neighbourhood.
ties are those ofcontinuity=====Sigmund Freud=====/* In what have been called his two "[[topology|topographies]]" (the first dating from 1900 and the second from 1923), contiguity [[Freud]] resorted to [[schema]]s to [[represent]] the various parts of the [[psychic apparatus]] and delimitationtheir interrelations. The notion of These schemas implicitly posited an equivalence between [[psychic]] space and Euclidean space in. */
topology [[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]] is different from that of waking ideational [[life]] and proposes the concept of '[[psychical]] locality'. [[Freud]] is careful to explain that this concept is a purely topographical one of topological space, which is and must not limited to Euclidean be confused with [[physical]] locality in any [[anatomical]] fashion.<ref>Freud, 1900a: SE V, 536</ref> His "[[topology|first topography]]" [[divided]] the [[psyche]] into three systems: the [[conscious]] (Cs), the [[preconscious]] ([[Pcs]]) and the [[unconscious]] (two-[[Ucs]]). The "[[topology|second topography]]" divided the [[psyche]] into the three [[agencies]] of the [[ego]], the [[superego]] and the [[id]].
[[Lacan]] criticizes these models for not [[being]] [[topological]] enough. He argues that the diagram with which [[Freud]] had illustrated his second topology in ''[[The Ego and threethe Id]]'' (1923b) led the majority of [[Freud]]'s readers to forget the [[analysis]] on which it was based because of the intuitive [[power]] of the [[image]].<ref>{{E}} p. 214</ref> [[Lacan]]'s interest in [[topology]] arises, then, because he sees it as providing a non-dimensional space)intuitive, nor even purely [[intellectual]] means of expressing the concept of [[structure]] that is so important to spaces his focus on the [[symbolic order]]. It is thus the task of [[Lacan]]'s topological models "to forbid [[imaginary]] [[capture]]."<ref>{{E}} p. 333</ref> Unlike intuitive [[images]], in which can be said to have a"[[perception]] eclipses structure", in [[Lacan]]'s [[topology]] "there is no occultation of the [[symbolic]]."<ref>{{E}} p. 333</ref>
dimension at all=====Structure=====[[Lacan]] argues that [[topology]] is not simply a [[metaphor]]ical way of expressing the concept of [[structure]]; it is [[structure]] itself. Topological space thus dispenses <ref>{{L}} "[[Works of Jacques Lacan|L'Étourdit]]," ''[[Scilicet]]'', no. 4, 1973: pp. 5-52</ref> He emphasizes that [[topology]] privileges the function of the cut (''[[coupure]]''), since the cut is what distinguishes a discontinuous transformation from a continuous one. Both kinds of transformation play a [[role]] in [[psychoanalytic treatment]]. As an example of a continuous transformation, [[Lacan]] refers to the [[moebius strip]]; just as one passes from one side to the [[other]] by following the [[strip]] round continuously, so the [[subject]] can [[traverse]] the [[fantasy]] without making a [[mythical]] leap from [[inside]] to [[outside]]. As an example of a discontinous transformation, [[Lacan]] also refers to the [[moebius strip]], which when cut down the middle is transformed into a single loop with all references tovery different topological properties; it now has two sides instead of one. Just as the cut operates a discontinuous transformation in the [[moebius strip]], so an effective [[interpretation]] proferred by the [[analyst]] modifies the [[structure]] of the [[analysand]]'s [[discourse]] in a radical way.
distance=====Figures=====While [[schema L]] and the other [[schemata]] which are produced in the 1950s can be seen as [[Lacan]]'s first incursion into [[topology]], topological forms only come into prominence when, in the 1960s, he turns his attention to the figures of the [[torus]], the [[moebius strip]], size[[Klein]]'s bottle, area and anglethe [[cross-cap]].<ref>{{L}} ''[[Works of Jacques Lacan|Le Séminaire. Livre IX. L'identification, 1961-62]]'', and is based only unpublished.</ref> Later on a concept , in the 1970s, [[Lacan]] turns his attention to the more [[complex]] area of closeness or[[knot]] [[theory]], especially the [[Borromean knot]].
neighbourhood.=====See Also====={{See}}* [[Borromean knot]]* [[Moebius strip]]{{Also}}
Freud used spatial metaphors to describe the psyche in The Interpretation of==References==<references/>[[Category:Psychoanalysis]][[Category:Jacques Lacan]][[Category:Dictionary]][[Category:Concepts]][[Category:Terms]]
Dreams, where he cites G. T. Fechner's idea that the scene of action of dreams is different from that of waking ideational life and proposes the concept of 'psychical locality'. Freud is careful to explain that this concept is a purely topographical one, and must not be confused with physical locality in any anatomical fashion (Freud, 1900a: SE V, 536). His 'first topography' (usually referred to in English as 'the topographic system') divided the psyche into three systems: the conscious (Cs), the preconscious (Pcs) and the unconscious (Ucs). The 'second topography' (usually referred to in English as 'the struc- tural system') divided the psyche into the three agencies of the ego, the superego and the id. Lacan criticises these models for not being topological enough. He argues that the diagram with which Freud had illustrated his second topology in The Ego and the Id (1923b) led the majority of Freud's readers to forget the analysis on which it was based because of the intuitive power of the image (see E, 214). Lacan's interest in topology arises, then, because he sees it as providing a non-intuitive, purely intellectual means of expressing the concept of STRUCTURE that is so important to his focus on the symbolic order. It is thus the task of Lacan's topological models 'to forbid imaginary capture' (E, 333). Unlike intuitive images, in which 'perception eclipses structure', in Lacan's topology 'there is no occultation of the symbolic' (E, 333). Lacan argues that topology is not simply a metaphorical way of expressing the concept of structure; it is structure itself (Lacan, 1973b). He emphasises that topology privileges the function of the cut (coupure), since the cut is what distinguishes a discontinuous transformation from a continuous one. Both kinds of transformation play a role in psychoanalytic treatment. As an exam- ple of a continuous transformation, Lacan refers to the MOEBIUS STRIP; j¸St SS one passes from one side to the other by following the strip round continu- ously, so the subject can traverse the fantasy without making a mythical leap from inside to outside. As an example of a discontinous transformation, Lacan also refers to the moebius strip, which when cut down the middle is trans- formed into a single loop with very different topological properties; it now has two sides instead of one. Just as the cut operates a discontinuous transforma- tion in the moebius strip, so an effective interpretation proferred by the analyst modifies the structure of the analysand's discourse in a radical way. While SCHEMA L and the other schemata which are produced in the 1950s can be seen as Lacan's first incursion into topology, topological forms only come into prominence when, in the 1960s, he turns his attention to the figures of the TORUs, the moebius strip, Klein's bottle, and the cross-cap (see Lacan, 1961-2). Later on, in the 1970s, Lacan turns his attention to the more complex area of knot theory, especially the BORROMEAN KNOT. For an introduction to Lacan's use of topological figures, see Granon-Lafont (1985).__NOTOC__
