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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.
=====Toplogical Space=====The [[Topologynotion]] refers primarily to the branch of [[mathematicstopology|space]] in [[topology]] that rigorously treats questions is one of neighborhoods[[topology|topological space]], limitswhich 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 continuityangle, and is based only on a [[concept]] of closeness or neighbourhood.
=====Sigmund Freud=====/* In what have been called his two "[[Psychoanalyststopology|topographies]] have applied it " (the first dating from 1900 and the second from 1923), [[Freud]] resorted to [[schema]]s to [[represent]] the study various parts of the [[unconsciouspsychic apparatus]] and their interrelations. These schemas implicitly posited an equivalence between [[structurepsychic]]sspace and Euclidean 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]] 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 "[[topology|first topography]]" [[divided]] the [[psyche]] into three systems: the [[conscious]] (Cs), the [[preconscious]] ([[Pcs]]) and the [[unconscious]] ([[Ucs]]). The "[[topology|second topography]]" divided the [[psyche]] into the three [[agencies]] of the [[ego]], the [[superego]] and the [[id]].
[[TopologyLacan]] (criticizes these models for not [[being]] [[topological]] enough. He argues that the diagram with which [[Freud]] had illustrated his second topology in ''topologie[[The Ego and the Id]]''(1923b) is a branch led the majority of [[mathematicsFreud]]'s readers to forget the [[analysis]] on which deals with it was based because of the properties intuitive [[power]] of figures in space which are preserved under all continuous deformationsthe [[image]].These properties are those of continuity, contiguity and delimitation<ref>{{E}} p. The notion of space 214</ref> [[Lacan]]'s interest in [[topology is one of topological space]] arises, then, which is not limited to Euclidean (twobecause he sees it as providing a non- and three-dimensional space)intuitive, nor even purely [[intellectual]] means of expressing the concept of [[structure]] that is so important to spaces which can be said his focus on the [[symbolic order]]. It is thus the task of [[Lacan]]'s topological models "to have a dimension at allforbid [[imaginary]] [[capture]]."<ref>{{E}} p. 333</ref> Topological space thus dispenses with all references to distanceUnlike intuitive [[images]], sizein which "[[perception]] eclipses structure", area and angle, and in [[Lacan]]'s [[topology]] "there is based only on a concept no occultation of closeness or neighbourhoodthe [[symbolic]]."<ref>{{E}} p.333</ref>
=====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 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.
==Freud===Figures=====In what have been called his two "topographies" (the first dating from 1900 While [[schema L]] and the second from 1923), other [[Freudschemata]] resorted to which are produced in the 1950s can be seen as [[schemaLacan]]'s first incursion into [[topology]], topological forms only come into prominence when, in the 1960s, he turns his attention to represent the various parts figures of the [[psychic apparatustorus]], the [[moebius strip]], [[Klein]] 's bottle, and their interrelationsthe [[cross-cap]].<ref>{{L}} ''[[Works of Jacques Lacan|Le Séminaire. Livre IX. L'identification, 1961-62]]'', unpublished. These schemas implicitly posited an equivalence between </ref> Later on, in the 1970s, [[Lacan]] turns his attention to the more [[complex]] area of [[knot]] [[psychic spacetheory]] and , especially the [[Euclidean spaceBorromean knot]].
==References==
<references/>
[[Category:Jacques Lacan]]
[[Category:MathematicsDictionary]][[Category:Concepts]]
[[Category:Terms]]