Some Sufficient Conditions for Maximal-Resolvability(1)
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 191-196
Voir la notice de l'article provenant de la source Cambridge University Press
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).
Pearson, T. L. Some Sufficient Conditions for Maximal-Resolvability(1). Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 191-196. doi: 10.4153/CMB-1971-034-5
@article{10_4153_CMB_1971_034_5,
author = {Pearson, T. L.},
title = {Some {Sufficient} {Conditions} for {Maximal-Resolvability(1)}},
journal = {Canadian mathematical bulletin},
pages = {191--196},
year = {1971},
volume = {14},
number = {2},
doi = {10.4153/CMB-1971-034-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-034-5/}
}
[1] 1. Ceder, J. G., On maximally resolvable spaces, Fund. Math. LV (1964), 87-93. Google Scholar
[2] 2. Ceder, J. G. and Pearson, T. L., On products of maximally resolvable spaces, Pacific J. Math. 22 (1967), 31-45. Google Scholar
[3] 3. Katětov, M., On topological spaces containing no disjoint dense subsets, Mat. Sbornik, N.S. (63) 21 (1947), 3-12. Google Scholar
[4] 4. Kelley, J. L., General topology, Van Nostrand, Princeton, N.J., 1955. Google Scholar
Cité par Sources :