The ideal generated by σ-nowhere dense sets

Jiling Cao; Sina Greenwood

doi:10.4995/agt.2006.1928

Authors

Jiling Cao University of Auckland
Sina Greenwood University of Auckland

DOI:

https://doi.org/10.4995/agt.2006.1928

Keywords:

Compatible, Ideal, Resolvable, σ-nowhere dense, Volterra, Weakly Volterra

Abstract

In this paper, we consider the ideal I_σ generated by all σ-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that I_σ is compatible with the topology for any given topological space, an analogue to the Banach category theorem. Some applications of this result and the Banach category theorem are also given.

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Author Biographies

Jiling Cao, University of Auckland

Department of Mathematics

Sina Greenwood, University of Auckland

Department of Mathematics

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