# zbMATH — the first resource for mathematics

A topological version of the Schauder theorem. (English) Zbl 0952.54030
The author introduces a class of topological spaces which he calls perfectly connected. Namely, a Hausdorff topological space $$X$$ is said to be perfectly $$\infty$$-connected provided it has a base $$B$$ (of its topology) which is closed with respect to finite intersections and consists of infinitely connected sets. Then the Schauder fixed-point theory is taken up to compact mappings of perfectly $$\infty$$-connected spaces.
##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 55M20 Fixed points and coincidences in algebraic topology
##### Keywords:
perfectly connected spaces
Full Text: