Brouwer Invariance of Domain Theorem

Pole DC	Wartość	Język
dc.contributor.author	Pąk, Karol	-
dc.date.accessioned	2015-12-09T20:40:37Z	-
dc.date.available	2015-12-09T20:40:37Z	-
dc.date.issued	2014	-
dc.identifier.citation	Formalized Mathematics, Volume 22, Issue 1, 2014, Pages 21-28	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3699	-
dc.description.abstract	In this article we focus on a special case of the Brouwer invariance of domain theorem. Let us A, B be a subsets of εn, and f : A → B be a homeomorphic. We prove that, if A is closed then f transform the boundary of A to the boundary of B; and if B is closed then f transform the interior of A to the interior of B. These two cases are sufficient to prove the topological invariance of dimension, which is used to prove basic properties of the n-dimensional manifolds, and also to prove basic properties of the boundary and the interior of manifolds, e.g. the boundary of an n-dimension manifold with boundary is an (n − 1)-dimension manifold. This article is based on [18]; [21] and [20] can also serve as reference books.	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	continuous transformations	-
dc.subject	topological dimension	-
dc.title	Brouwer Invariance of Domain Theorem	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2014-0003	-
dc.description.Affiliation	Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland	-
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