On the size of a map


	Open access
	On the size of a map


	Fixed Point Theory, Volume 19, No. 2, 2018, 595-610, June 1st, 2018 DOI: 10.24193/fpt-ro.2018.2.47 Authors: Adam Idzik, Władysław Kulpa and Piotr Maćkowiak Abstract: Some properties depending on an upper bound of the diameter of fibers of a continuous map ƒ from the n-dimensional unit cube Iⁿ to the Euclidean space are investigated. In particular, we consider the problem when the image ƒ(Iⁿ) has the nonempty interior. Obtained results are consequences of the Poincaré theorem and some theorems on extensions of maps. Generalizations of the De Marco theorem and the Borsuk theorem are presented. Key Words and Phrases: Domain invariance theorem, Bolzano-Poincaré theorem, Brouwer fixed point theorem, size of a map. 2010 Mathematics Subject Classification: 54H25, 55M20, 54F45, 54B25. Published on-line: June 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents

Home | Indexing-Abstracting | Aims and Scope | Editors | Editorial Board | Published Volumes | Instructions for authors | Subscription | Reviewers Ackn. | Secretaries | FPT Conferences | FPT Book Review