Kulpa, W. A topological version of the Schauder theorem. (English) Zbl 0952.54030 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 PDF BibTeX XML Cite \textit{W. Kulpa}, Acta Univ. Carol., Math. Phys. 40, No. 2, 85--89 (1999; Zbl 0952.54030) Full Text: EuDML OpenURL