Some Sufficient Conditions for Maximal-Resolvability(1)
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 191-196
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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).
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/}
}
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