"[[Topology]]" ([[Fr]]. ''{{Top}}[[topologie]]'') is a branch of [[mathematics]] which deals with the properties of figures in space where are preserved under all continuous deformations.{{Bottom}}
=====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 is not limited to Euclidean (two- and [[three]]-dimensional [[space]]), nor even to spaces which can be said to have a [[dimension ]] at all. [[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.
Topological space thus dispenses with all references =====Sigmund Freud=====/* In what have been called his two "[[topology|topographies]]" (the first dating from 1900 and the second from 1923), [[Freud]] resorted to [[schema]]s to distance, size, area [[represent]] the various parts of the [[psychic apparatus]] and angle, their interrelations. These schemas implicitly posited an equivalence between [[psychic]] space and is based only on a concept of closeness or neighbourhoodEuclidean space.*/
==[[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==In what have been called his two ]] is careful to explain that this concept is a purely topographical one, and must not be confused with [[physical]] locality in any [[anatomical]] fashion.<ref>Freud, 1900a: SE V, 536</ref> His "topographies[[topology|first topography]]" [[divided]] the [[psyche]] into three systems: the [[conscious]] (Cs), the first dating from 1900 [[preconscious]] ([[Pcs]]) and the second from 1923[[unconscious]] ([[Ucs]]), . The "[[Freudtopology|second topography]] resorted to " divided the [[schemapsyche]]s to represent into the various parts three [[agencies]] of the [[psychic apparatusego]], the [[superego]] and their interrelationsthe [[id]].
These schemas implicitly posited an equivalence between psychic space [[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 Euclidean spacethe 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-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]]."<ref>{{E}} p. 333</ref> Unlike intuitive [[images]], in which "[[perception]] eclipses structure", in [[Lacan]]'s [[topology]] "there is no occultation of the [[symbolic]]."<ref>{{E}} p.333</ref>
=====Structure=====[[FreudLacan]] used spatial metaphors to describe argues that [[topology]] is not simply a [[metaphor]]ical way of expressing the psyche in concept of [[structure]]; it is [[structure]] itself.<ref>{{L}} "[[Works of Jacques Lacan|L'Étourdit]]," ''[[The Interpretation of DreamsScilicet]]'', where he cites Gno. T4, 1973: pp. Fechner5-52</ref> He emphasizes that [[topology]] privileges the function of the cut ('s idea that '[[coupure]]''), since the scene cut is what distinguishes a discontinuous transformation from a continuous one. Both kinds of action transformation play a [[role]] in [[psychoanalytic treatment]]. As an example of dreams 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 very different from that topological properties; it now has two sides instead of waking ideational life and proposes one. Just as the cut operates a discontinuous transformation in the [[moebius strip]], so an effective [[interpretation]] proferred by the [[analyst]] modifies the concept [[structure]] of the [[analysand]]'psychical locality's [[discourse]] in a radical way.
=====Figures=====While [[Freudschema L]] is careful 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 explain that this concept is a purely topographical onethe figures of the [[torus]], the [[moebius strip]], [[Klein]]'s bottle, and must not be confused with physical locality in any anatomical fashionthe [[cross-cap]].<ref>Freud{{L}} ''[[Works of Jacques Lacan|Le Séminaire. Livre IX. L'identification, 1900a: SE V1961-62]]'', 536unpublished.</ref> Later on, in the 1970s, [[Lacan]] turns his attention to the more [[complex]] area of [[knot]] [[theory]], especially the [[Borromean knot]].
His 'first topography' divided the =====See Also====={{See}}* [[psycheBorromean knot]] into three systems: the * [[consciousMoebius strip]] (Cs), the [[preconscious]] (Pcs) and the [[unconscious]] (Ucs). {{Also}}
The 'second topography' divided the [[psyche]] into the three agencies of the [[ego]], the [[superego]] and the [[id]]. [[Lacan]] criticises these models for not being [[topological]] enough. ==References==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.<ref>{{E}} p.214<references/ref> [[LacanCategory:Psychoanalysis]]'s interest in [[topologyCategory:Jacques Lacan]] arises, then, because he sees it as providing a non-intuitive, purely intellectual means of expressing the concept of [[structureCategory:Dictionary]] that is so important to his focus on the [[symbolic order]]. It is thus the task of [[LacanCategory:Concepts]]'s topological models "to forbid imaginary capture."<ref>{{E}} p.333</ref> Unlike intuitive images, in which "perception eclipses structure", in [[Lacan]Category:Terms]'s [[topology]] "there is no occultation of the symbolic."<ref>{{E}} p.333</ref> --
[[Lacan]] argues that [[topology]] is not simply a [[metaphor]]ical way of expressing the concept of [[structure]]; it is [[structure]] itself.<ref>Lacan, 1973b</ref> 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 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 very 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. -- 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]].<ref>Lacan. 1961-2</ref> Later on, in the 1970s, [[Lacan]] turns his attention to the more complex area of knot theory, especially the [[borromean knot]]. [[Category:Dictionary]]__NOTOC__
