What is Topology?

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The term 'deconstruction', refers in the first instance to the way in which the 'accidental' features of a text can be seen as betraying, subverting, its purportedly 'essential' message.

Deconstructionist Theory

By

Richard Rorty

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The Real Line and the Open Unit Interval

We have indicated that from a topological point of view and are indistinguishable, their perceived difference is an " 'accidental' feature" of how we choose to measure the underlying topological space. In this section of the course, we will make precise the term "indistinguishable."

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The Cylinder in 3-space and in the Plane

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The Torus (from Crossley's notes)

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The Möbius Band and the Klein Bottle

Constructing the Klein Bottle:

Start with the Cylinder:

and identify

Letting be the Klein Bottle and holding constant , note that the path where

goes from to So you have to go around twice to get back to where you started!

Unlike the Cylinder the Möbius Band cannot be embedded in the plane, and unlike the Torus the Klein Bottle cannot be embedded in 3-space.

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We will also want to study topological spaces ignoring the " 'accidental' features" of how we choose to embed them in some Euclidian Space.