Equivalent forms of the Brouwer fixed point theorem II
Copyright policy )Equivalent forms of the Brouwer fixed point theorem II
The authors extend characterizations of the celebrated Brouwer fixed point theorem presented in their earlier paper [Topol. Methods Nonlinear Anal. 44, No. 1, 263--276 (2014; Zbl 1476.54070)]. Firstly, some equivalent versions of the labeled Sperner lemma are provided. Then, it is proved that an indexed closed (open) cover theorem, the Eilenberg-Otto theorem, the Poincaré theorem and the Bohl-Brouwer theorem are equivalent. A lemma on the collapse is also proved, and finally, the Steinhaus chessboard theorem and the Gale theorem on hexagonal tiling are generalized.
Fixed-point and coincidence theorems (topological aspects), Connections of general topology with other structures, applications, Steinhaus chessboard problem, Brouwer fixed point theorem
Fixed-point and coincidence theorems (topological aspects), Connections of general topology with other structures, applications, Steinhaus chessboard problem, Brouwer fixed point theorem
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!