Brouwer Invariance of Domain Theorem

• Autorzy: Karol Pąk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

continuous transformations; topological dimension

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2014
• Tom: 22
• Numer: 1
• Strony: 21-28

Twórcy

autor

Karol Pąk

• Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland

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Identyfikatory

DOI

10.2478/forma-2014-0003