Original scientific paper

A selection theorem for simplex-valued maps

Ivan Ivanšić
Leonard R. Rubin

Abstract

The purpose of this short note is to prove the following theorem. Let X be a hereditarily normal paracompact Hausdorff space, K be a simplicial complex, and : X K be a function. Suppose that {U | } and {f | } are collections such that for each , f is a map of U to |K|, and if x U, then f(x) (x). Assume further that {U | } is an open cover of X. Then there exists a map f : X |K| such that for each x X, f(x) (x).

Keywords

Contiguous functions; continuous function; hereditarily paracompact; polyhedron; selection; simplex; simplicial complex; stratifiable space

Hrčak ID:

1255

URI

https://hrcak.srce.hr/1255

Publication date:

29.11.2004.

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