Re: subset of contractible

From: William Elliot <marsh@xxxxxxxxxxxxxxxxxx>
Date: Wed, 11 Jul 2007 03:11:43 -0700

On Wed, 11 Jul 2007, Sonya84 wrote:

Suppose X is a contractible topological space
and S subset of X is a topological subspace of X.

Is S contractible itself?

No. Every multi-point contractible space has non-contractible two point
subspaces such as the closed unit interval and it's endpoints.

Consider also the real plane and the unit circle or real three space and
the unit sphere.
.

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- Re: subset of contractible
  - From: Zbigniew Karno

References:
- subset of contractible
  - From: Sonya84

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Re: subset of contractible
... and S subset of X is a topological subspace of X. ... Every multi-point contractible space has non-contractible two point ... Consider also the real plane and the unit circle or real three space and ... The real plane P^2 is not contractible, ...
(sci.math)
Re: subset of contractible
... Sonya84 wrote: ... and S subset of X is a topological subspace of X. ... How about the opposite? ... Suppose S is ANY topological space. ...
(sci.math)