TOPOLOGY (384) {{Top}}[CD[topologie]]{{Bottom}}
=====Definition====="[[Topology]]" is a branch of [[mathematics]] which deals with the properties of [[figures]] in [[topology (topologie) Topology (originally called analysis situs by|space]] where are preserved under all continuous deformations. These properties are those of continuity, contiguity and delimitation.
Leibniz) =====Toplogical Space=====The [[notion]] of [[topology|space]] in [[topology]] is a branch one of mathematics [[topology|topological space]], which deals 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 the properties all references to distance, size, area and angle, and is based only on a [[concept]] of figurescloseness or neighbourhood.
in =====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 [[represent]] the various parts of the [[psychic apparatus]] and their interrelations. These schemas implicitly posited an equivalence between [[psychic]] space and Euclidean space which are preserved under all continuous deformations. These proper-*/
ties are those ofcontinuity[[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, contiguity and delimitationmust 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 the [[unconscious]] ([[Ucs]]). The notion "[[topology|second topography]]" divided the [[psyche]] into the three [[agencies]] of space inthe [[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 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</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 one so important to his focus on the [[symbolic order]]. It is thus the task of [[Lacan]]'s topological spacemodels "to forbid [[imaginary]] [[capture]]."<ref>{{E}} p. 333</ref> Unlike intuitive [[images]], in which "[[perception]] eclipses structure", in [[Lacan]]'s [[topology]] "there is not limited to Euclidean (two-no occultation of the [[symbolic]]."<ref>{{E}} p. 333</ref>
and three=====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-dimensional space52</ref> He emphasizes that [[topology]] privileges the function of the cut (''[[coupure]]''), nor even 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 spaces which the [[moebius strip]]; just as one passes from one side to the [[other]] by following the [[strip]] round continuously, so the [[subject]] can be said [[traverse]] the [[fantasy]] without making a [[mythical]] leap from [[inside]] to [[outside]]. As an example of a discontinous transformation, [[Lacan]] also refers to have 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 aradical way.
dimension at all=====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]], [[Klein]]'s bottle, and the [[cross-cap]]. Topological space thus dispenses with all references <ref>{{L}} ''[[Works of Jacques Lacan|Le Séminaire. Livre IX. L'identification, 1961-62]]'', unpublished.</ref> Later on, in the 1970s, [[Lacan]] turns his attention tothe more [[complex]] area of [[knot]] [[theory]], especially the [[Borromean knot]].
distance, size, area and angle, and is based only on a concept of closeness or=====See Also====={{See}}* [[Borromean knot]]* [[Moebius strip]]{{Also}}
neighbourhood.==References==<references/>[[Category:Psychoanalysis]][[Category:Jacques Lacan]][[Category:Dictionary]][[Category:Concepts]][[Category:Terms]]
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, 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). topology, 22, 34, 74, 89-90, 131, 144, 147, 155-6, 161, 164, 181-2, 184, 203, 206, 209, * 235, 244-5, 257, 270-1 [[Seminar XI]]__NOTOC__
