Science and Art in Representing the Fifth Dimension

Tijana T. Ivancevic; Nick N. Ivancevic; Sasa A. Jovanovic

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Brouwer Invariance of Domain Theorem

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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...