REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU
UwB

Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3699
Pełny rekord metadanych
Pole DCWartośćJęzyk
dc.contributor.authorPąk, Karol-
dc.date.accessioned2015-12-09T20:40:37Z-
dc.date.available2015-12-09T20:40:37Z-
dc.date.issued2014-
dc.identifier.citationFormalized Mathematics, Volume 22, Issue 1, 2014, Pages 21-28-
dc.identifier.issn1426-2630-
dc.identifier.issn1898-9934-
dc.identifier.urihttp://hdl.handle.net/11320/3699-
dc.description.abstractIn 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.isoen-
dc.publisherDe Gruyter Open-
dc.subjectcontinuous transformations-
dc.subjecttopological dimension-
dc.titleBrouwer Invariance of Domain Theorem-
dc.typeArticle-
dc.identifier.doi10.2478/forma-2014-0003-
dc.description.AffiliationInstitute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland-
dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.-
dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.-
dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.-
dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.-
dc.description.referencesLeszek Borys. Paracompact and metrizable spaces. Formalized Mathematics, 2(4):481-485, 1991.-
dc.description.referencesCzesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.-
dc.description.referencesCzesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.-
dc.description.referencesCzesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.-
dc.description.referencesCzesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.-
dc.description.referencesCzesław Bylinski. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.-
dc.description.referencesCzesław Bylinski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.-
dc.description.referencesCzesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.-
dc.description.referencesCzesław Bylinski and Piotr Rudnicki. Bounding boxes for compact sets in E2. Formalized Mathematics, 6(3):427-440, 1997.-
dc.description.referencesAgata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.-
dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.-
dc.description.referencesAgata Darmochwał. Families of subsets, subspaces and mappings in topological spaces. Formalized Mathematics, 1(2):257-261, 1990.-
dc.description.referencesAgata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.-
dc.description.referencesRoman Duda. Wprowadzenie do topologii. PWN, 1986.-
dc.description.referencesNoboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.-
dc.description.referencesRyszard Engelking. Dimension Theory. North-Holland, Amsterdam, 1978.-
dc.description.referencesRyszard Engelking. General Topology. Heldermann Verlag, Berlin, 1989.-
dc.description.referencesZbigniew Karno. Continuity of mappings over the union of subspaces. Formalized Mathematics, 3(1):1-16, 1992.-
dc.description.referencesZbigniew Karno. Separated and weakly separated subspaces of topological spaces. Formalized Mathematics, 2(5):665-674, 1991.-
dc.description.referencesArtur Korniłowicz. Homeomorphism between [:EiT , EjT :] and E(i+j)T . Formalized Mathematics, 8(1):73-76, 1999.-
dc.description.referencesArtur Korniłowicz. On the continuity of some functions. Formalized Mathematics, 18(3): 175-183, 2010. doi:10.2478/v10037-010-0020-z.-
dc.description.referencesArtur Korniłowicz. Arithmetic operations on functions from sets into functional sets. Formalized Mathematics, 17(1):43-60, 2009. doi:10.2478/v10037-009-0005-y.-
dc.description.referencesArtur Korniłowicz and Yasunari Shidama. Brouwer fixed point theorem for disks on the plane. Formalized Mathematics, 13(2):333-336, 2005.-
dc.description.referencesArtur Korniłowicz and Yasunari Shidama. Intersections of intervals and balls in EnT. Formalized Mathematics, 12(3):301-306, 2004.-
dc.description.referencesArtur Korniłowicz and Yasunari Shidama. Some properties of circles on the plane. Formalized Mathematics, 13(1):117-124, 2005.-
dc.description.referencesEugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.-
dc.description.referencesRoman Matuszewski and Yatsuka Nakamura. Projections in n-dimensional Euclidean space to each coordinates. Formalized Mathematics, 6(4):505-509, 1997.-
dc.description.referencesRobert Milewski. Bases of continuous lattices. Formalized Mathematics, 7(2):285-294, 1998.-
dc.description.referencesBeata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.-
dc.description.referencesKarol Pak. The rotation group. Formalized Mathematics, 20(1):23-29, 2012. doi:10.2478/v10037-012-0004-2.10.2478/v10037-012-0004-2-
dc.description.referencesKarol Pak. Small inductive dimension of topological spaces. Formalized Mathematics, 17 (3):207-212, 2009. doi:10.2478/v10037-009-0025-7.-
dc.description.referencesKarol Pak. Small inductive dimension of topological spaces. Part II. Formalized Mathematics, 17(3):219-222, 2009. doi:10.2478/v10037-009-0027-5.-
dc.description.referencesAndrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.-
dc.description.referencesAndrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.-
dc.description.referencesAndrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.-
dc.description.referencesMichał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.-
dc.description.referencesWojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.-
dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.-
dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.-
dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.-
dc.description.referencesMirosław Wysocki and Agata Darmochwał. Subsets of topological spaces. Formalized Mathematics, 1(1):231-237, 1990.-
dc.description.referencesMariusz Zynel and Adam Guzowski. T0 topological spaces. Formalized Mathematics, 5 (1):75-77, 1996.-
Występuje w kolekcji(ach):Artykuły naukowe (WMiI)
Formalized Mathematics, 2014, Volume 22, Issue 1

Pliki w tej pozycji:
Plik Opis RozmiarFormat 
forma-2014-0003.pdf295,63 kBAdobe PDFOtwórz
Pokaż uproszczony widok rekordu Zobacz statystyki


Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL Creative Commons