Re: subset of contractible

From: "G. A. Edgar" <edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
Date: Wed, 11 Jul 2007 07:47:52 -0400

In article <1184146904.357990.268590@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Sonya84 <sonianardi84@xxxxxxxxx> wrote:

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

Is S contractible itself?

Since X is contractible we have that X is pathwise-connected, so -
without loss of generality - we can suppose X is homotopically
equivalent to a point p in S.

Sonia

How about the opposite? Suppose S is ANY topological space.
Then S can be embedded in some contractible space X.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.

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References:
- subset of contractible
  - From: Sonya84

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