Talk:Fixed-point property
 | This article is rated Start-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
| |||||||||||
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)