Displaying similar documents to “Bisectors in Minkowski 3-space.”

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].

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...

Tietze Extension Theorem for n-dimensional Spaces

Karol Pąk (2014)

Formalized Mathematics

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In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic...