A topological version of the Schauder theorem. (English) Zbl 0952.54030

Kulpa, W.

Acta Univ. Carol., Math. Phys. 40, No. 2, 85-89 (1999).

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.

Reviewer: Lech Górniewicz (Toruń)

MSC:

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

Keywords:

perfectly connected spaces