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Some Sufficient Conditions for Maximal-Resolvability(1)

Published online by Cambridge University Press:  20 November 2018

T. L. Pearson
T. L. Pearson*
Affiliation:
Acadia University, Wolfville, Nova Scotia
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A topological space X is called maximally resolvable if it admits a largest possible family of pairwise disjoint, “maximally dense” subsets. More precisely, if Δ(X) denotes the least among the cardinal numbers of the nonvoid open subsets of X, then X is maximally resolvable if it has isolated points or there exists a family {R α}α < Δ(X) of subsets of X, called a maximal resolution for X, such that ∪{R α | α < Δ(X)} = X, Rγ ∩ Rδ==ϕ if γ ≠ δ, and, for each a and each nonvoid open subset V of X, the cardinality of R α ∩ V is not less than Δ(X).

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 191 - 196
Copyright
Copyright © Canadian Mathematical Society 1971

Footnotes

(1)

This research was partially supported by the Summer Research Institute of the Canadian Mathematical Congress.

References

1. Ceder, J. G., On maximally resolvable spaces, Fund. Math. LV (1964), 87-93.Google Scholar
2. Ceder, J. G. and Pearson, T. L., On products of maximally resolvable spaces, Pacific J. Math. 22 (1967), 31-45.Google Scholar
3. Katětov, M., On topological spaces containing no disjoint dense subsets, Mat. Sbornik, N.S. (63) 21 (1947), 3-12.Google Scholar
4. Kelley, J. L., General topology, Van Nostrand, Princeton, N.J., 1955.Google Scholar