Displaying similar documents to “Topological Manifolds”

On foliations in Sikorski differential spaces with Brouwerian leaves

Włodzimierz Waliszewski (1991)

Annales Polonici Mathematici

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The class of locally connected and locally homeomorphically homogeneous topological spaces such that every one-to-one continuous mapping of an open subspace into the space is open has been considered. For a foliation F [3] on a Sikorski differential space M with leaves having the above properties it is proved that for some open sets U in M covering the set of all points of M the connected components of U ∩ L̲ in the topology of M coincide with the connected components in the topology...

Brouwer Invariance of Domain Theorem

Karol Pąk (2014)

Formalized Mathematics

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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...

Brouwer Fixed Point Theorem in the General Case

Karol Pąk (2011)

Formalized Mathematics

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In this article we prove the Brouwer fixed point theorem for an arbitrary convex compact subset of εn with a non empty interior. This article is based on [15].