Original scientific paper

A local to global selection theorem for simplex-valued functions

Ivan Ivanšić
Leonard R. Rubin

Abstract

Suppose we are given a function : X K where X is a paracompact space and K is a simplicial complex, and an open cover {U | } of X, so that for each , f : U |K| is a map that is a selection of on its domain. We shall prove that there is a map f : X |K| which is a selection of . We shall also show that under certain conditions on such a set of maps or on the complex K, there exists a : X K with the property that each f is a selection of on its domain and that there is a selection f : X |K| of . The term selection, as used herein, will always refer to a map f, i.e., continuous function, having the property that f(x) (x) for each x in the domain.

Keywords

Contiguous functions; continuous function; discrete collection; infinite simplex; K-modification; locally finite-dimensional complex; paracompact; polyhedron; principal simplex; selection; simplex; simplicial complex

Hrčak ID:

385

URI

https://hrcak.srce.hr/385

Publication date:

9.11.2005.

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