Kulpa, W. The indexed open covering theorem. (English) Zbl 0804.54012 Acta Univ. Carol., Math. Phys. 34, No. 2, 75-82 (1993). Given an indexed open cover \(\{U_ s : s \in S\}\) of the Tikhonov cube \(I^ S\) (where \(I = [0,1])\), there exists an index \(s \in S\) such that \(U_ s\) contains a connected subset which intersects both \(I^ +_ s = \{x_ s = 1\}\) and \(I_ s^ - = \{x_ s = - 1\}\). The author proves this statement called the ‘indexed open covering theorem’ and derives many important corollaries such as a new proof of the Bohl-Brouwer fixed point theorem. Reviewer: M.V.Matveev (Moskva) Cited in 1 Document MSC: 54B10 Product spaces in general topology 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:indexed open cover; cardinal dimension; Tychonoff cube; Tikhonov cube; Bohl-Brouwer fixed point theorem × Cite Format Result Cite Review PDF Full Text: EuDML