Glasnik Matematicki, Vol. 39, No.2 (2004), 331-333.

A SELECTION THEOREM FOR SIMPLEX-VALUED MAPS

Ivan Ivanšić and Leonard R. Rubin

I. Ivansic, Department of Mathematics, University of Zagreb, Unska 3, P.O. Box 148, 10001 Zagreb, Croatia
e-mail: ivan.ivansic@fer.hr

L. R. Rubin, Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
e-mail: lrubin@ou.edu


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 σ : X K be a function. Suppose that {Uα | α Γ} and {fα | α Γ} are collections such that for each α Γ, fα is a map of Uα to |K|, and if x Uα, then fα(x) σ(x). Assume further that {Uα | α Γ} is an open cover of X. Then there exists a map f : X |K| such that for each x X, f(x) σ(x).

2000 Mathematics Subject Classification.   54C65, 54C05, 54E20.

Key words and phrases.   Contiguous functions, continuous function, hereditarily paracompact, polyhedron, selection, simplex, simplicial complex, stratifiable space.


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