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Topologies Determined by -Ideals on ω1

Published online by Cambridge University Press:  20 November 2018

S. Broverman ,
J. Ginsburg ,
K. Kunen  and
F. D. Tall
S. Broverman
Affiliation:
University of Texas, Austin, Texas
J. Ginsburg
Affiliation:
University of Manitoba, Winnipeg, Manitoba
K. Kunen
Affiliation:
University of Wisconsin, Madison, Wisconsin
F. D. Tall
Affiliation:
University of Toronto, Toronto, Ontario
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σ-ideals (collections of sets which are closed under subset and countable union) are certainly important mathematically—consider first category sets, sets of measure zero, nonstationary sets, etc.—but aside from the observation that in certain spaces the first category σ-ideal is proper, cr-ideals have not been extensively studied by topologists. In this note we study a natural topology determined by a d-ideal, exploiting the interplay between the set-theoretic properties of the σ-ideal and the topological properties of the associated space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1306 - 1312
Copyright
Copyright © Canadian Mathematical Society 1978

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