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.


54H25 Fixed-point and coincidence theorems (topological aspects)
55M20 Fixed points and coincidences in algebraic topology
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