Viewing topic: Topological Dimension

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Topological Dimension

  • Definition: A space X is said to be finite dimensional if there is some integer m such that for every open covering A of X, there is an open covering B of X that refines A and has order m+1. The topological dimension of X is defined to be the smallest value of m for which this statement holds; we denote it by dim X.

    Source: Topology (second edition) by James R. Munkres

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