Talk:Fixed-point property
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What is meant by "universal" in the statement "A topological space has the fixed point property if and only if its identity map is universal."? Gandalf (talk) 17:08, 3 October 2008 (UTC)
- A map f: X -> Y is universal if for any map g: X -> Y there is a point x in X, such that f(x) = g(x). It's unclear whether it adds anything to the article since it's a tautology in this case. Terminus0 (talk) 02:10, 21 August 2011 (UTC)
Are there any examples of two spaces with the fixed point property whose product does not? Gandalf (talk) 17:15, 3 October 2008 (UTC)
Necessary condition[edit]
"In 1932 Borsuk asked whether compactness together with contractibility could be a necessary and sufficient condition for the FPP to hold." What does necessary mean here? Clearly, there are non-contractible spaces with FPP, such as even real projective spaces. Terminus0 (talk) 02:10, 21 August 2011 (UTC)