Vol. 105, No. 2, 1983

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Sup-characterization of stratifiable spaces

Carlos R. Borges and Gary Fred Gruenhage

Vol. 105 (1983), No. 2, 279–284
Abstract

We prove that a T1-space (X,τ) is stratifiable if and only if, for each U τ, one can find a continuous function fU : X I such that fU1(0) = X U and, for each 𝒰 ⊂ τ, supU∈𝒰fU is continuous. This result is closely related to characterizations of metrizable and paracompact spaces, by J. Nagata, and J. Guthrie and M. Henry.

Mathematical Subject Classification 2000
Primary: 54E20
Milestones
Received: 19 August 1981
Published: 1 April 1983
Authors
Carlos R. Borges
Gary Fred Gruenhage