Re: subset of contractible

On 11 Lip, 12:11, William Elliot <m...@xxxxxxxxxxxxxxxxxx> wrote:
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.

The real plane P^2 is not contractible,
moreover some circles in it are not
contractible in P^2.

Regards, Z. Karno


.

Relevant Pages

  • 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 ... The real plane P^2 is not contractible, ... R^2 strongly contracts to by homotopy ...
    (sci.math)
  • Re: subset of contractible
    ... On Wed, 11 Jul 2007, Sonya84 wrote: ... and S subset of X is a topological subspace of X. ... Consider also the real plane and the unit circle or real three space and ... the unit sphere. ...
    (sci.math)