Brouwer Invariance of Domain Theorem
Karol Pąk
Formalized Mathematics, Tome 22 (2014), p. 21-28 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:266703
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     author = {Karol P\k ak},
     title = {Brouwer Invariance of Domain Theorem},
     journal = {Formalized Mathematics},
     volume = {22},
     year = {2014},
     pages = {21-28},
     zbl = {1298.54004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0003}
}
Karol Pąk. Brouwer Invariance of Domain Theorem. Formalized Mathematics, Tome 22 (2014) pp. 21-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0003/

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