On irreducible spaces

Publisher: Cambridge University Press

E-ISSN: 1755-1633|12|1|143-148

ISSN: 0004-9727

Source: Bulletin of the Australian Mathematical Society, Vol.12, Iss.1, 1975-02, pp. : 143-148

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Abstract

A constructive proof of a theorem of Worrell and Wicke, which states that every open covering of a θ-refinable space has a σ-distributively point-finite open refinement that covers the space minimally, is presented. Spaces for which every open covering has an open refinement which covers the space minimally are characterized by the use of discrete closed collections and some open questions relating to spaces of this type are included.