Glasnik matematički, Vol. 39 No. 2, 2004.
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
Publication date:
29.11.2004.
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