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Topology

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{{Top}}[[topologie]]{{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.
These properties are those =====Toplogical Space=====The [[notion]] of continuity[[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, contiguity and delimitationis based only on a [[concept]] of closeness or neighbourhood.
==Space===Sigmund Freud=====The notion of space in /* In what have been called his two "[[topology|topographies]] is one of topological space, which is not limited to Euclidean " (two- the first dating from 1900 and three-dimensional spacethe second from 1923), nor even [[Freud]] resorted to spaces which can be said [[schema]]s to have a dimension at all[[represent]] the various parts of the [[psychic apparatus]] and their interrelations. These schemas implicitly posited an equivalence between [[psychic]] space and Euclidean space. */
Topological space thus dispenses with all references [[Freud]] used spatial metaphors to distancedescribe the psyche in ''[[The Interpretation of Dreams]]'', sizewhere 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, area and anglemust not 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 is based only on a concept the [[unconscious]] ([[Ucs]]). The "[[topology|second topography]]" divided the [[psyche]] into the three [[agencies]] of closeness or neighbourhoodthe [[ego]], the [[superego]] and the [[id]].
==[[Lacan]] criticizes these models for not [[being]] [[topological]] enough. He argues that the diagram with which [[Freud==In what have been called ]] had illustrated his two "topographies" (the first dating from 1900 second topology in ''[[The Ego and the second from 1923Id]]'' (1923b), led the majority of [[Freud]] resorted 's readers to forget the [[analysis]] on which it was based because of the intuitive [[power]] of the [[schemaimage]].<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 represent his focus on the [[symbolic order]]. It is thus the various parts 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 [[psychic apparatussymbolic]] and their interrelations. "<ref>{{E}} p. 333</ref>
These schemas implicitly posited =====Structure=====[[Lacan]] argues that [[topology]] is not simply a [[metaphor]]ical way of expressing the concept of [[structure]]; it is [[structure]] itself.<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 equivalence between psychic space and Euclidean spaceexample 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.
=====Figures=====While [[Freudschema L]] used spatial metaphors 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 describe the psyche in figures of the [[torus]], the [[moebius strip]], [[Klein]]'s bottle, and the [[cross-cap]].<ref>{{L}} ''[[The Interpretation Works of DreamsJacques Lacan|Le Séminaire. Livre IX. L'identification, 1961-62]]'', where he cites Gunpublished. T. Fechner's idea that </ref> Later on, in the 1970s, [[Lacan]] turns his attention to the scene more [[complex]] area of action of dreams is different from that of waking ideational life and proposes [[knot]] [[theory]], especially the concept of 'psychical locality'[[Borromean knot]].
[[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.<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 of the [[ego]], the [[superego]] and the [[id]]. [[Lacan]] criticises these models for not being [[topological]] enough. =====See Also=====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>{{ESee}} p.214</ref>  [[Lacan]]'s interest in * [[topologyBorromean knot]] 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 * [[LacanMoebius strip]]'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>{{EAlso}} 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.  --
==References==
<references/>
[[Category:Psychoanalysis]]
[[Category:Jacques Lacan]]
[[Category:Dictionary]]
[[Category:Concepts]]
[[Category:Terms]]
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__
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