Glasnik Matematicki, Vol. 40, No.2 (2005), 339-345.


Ivan Ivanšić and Leonard R. Rubin

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

Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA

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

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

Key words and phrases.   Contiguous functions, continuous function, discrete collection, infinite simplex, K-modification, locally finite-dimensional complex, paracompact, polyhedron, principal simplex, selection, simplex, simplicial complex.

Full text (PDF) (free access)

DOI: 10.3336/gm.40.2.14


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