Vol. 62, No. 2, 1976

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On irreducible spaces. II

James Robert Boone

Vol. 62 (1976), No. 2, 351–357
Abstract

A topological space is said to be irreducible if every open covering has an open refinement that covers the space minimally. Irreducibility is a fundamental property related to cardinality conditions for open coverings. In this paper, a constructive proof is presented to establish that the weak 𝜃-refinable spaces of Smith are irreducible. Various results concerning cardinality conditions for open coverings follow as corollaries. Some examples are included.

Mathematical Subject Classification 2000
Primary: 54D20
Milestones
Received: 11 April 1974
Revised: 22 October 1975
Published: 1 February 1976
Authors
James Robert Boone