http://www.netvouz.com/narky/tag/point?feed=rss narky's bookmarks tagged "point" on Netvouz http://planetmath.org/encyclopedia/AnyTopologicalSpaceWithTheFixedPointPropertyIsConnected.html Theorem Any topological space with the fixed-point property is connected. Proof. We will prove the contrapositive. .... Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups narky Fri, 27 Apr 2007 04:24:36 GMT http://en.wikipedia.org/wiki/Fixed_point_property In mathematics, a topological space X has the fixed point property if all continuous mappings from X to X have a fixed point. Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups narky Tue, 01 May 2007 02:50:22 GMT http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist_2001;task=show_msg;msg=0302 Does a space which has the finite closed topology have the fixed-point property? I really don't know how to go about this, but my initial thoughts are: - This should be related to continuous functions and connectedness. Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups narky Tue, 01 May 2007 02:24:24 GMT http://en.wikipedia.org/wiki/Fixed-point_theorem In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Results of this kind are amongst the most generally useful in mathematics. The Banach fixed point theorem gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point. By contrast, the Brouwer fixed point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point (See also Sperner's lemma). Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups narky Tue, 01 May 2007 02:51:32 GMT