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


Ivan Ivanšić and Leonard R. Rubin

I. Ivansic, Department of Mathematics, University of Zagreb, Unska 3, P.O. Box 148, 10001 Zagreb, Croatia

L. R. Rubin, Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA

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.

Full text (PDF) (free access)
Glasnik Matematicki Home Page