Sup-characterization of stratifiable spaces

Carlos R. Borges and Gary Fred Gruenhage

Vol. 105 (1983), No. 2, 279–284

DOI: 10.2140/pjm.1983.105.279

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 f_U : X → I such that f_U⁻¹(0) = X − U and, for each 𝒰 ⊂ τ, sup_U∈𝒰f_U 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