The Number of Compatible Totally Bounded Quasi-Uniformities
Tóm tắt
We prove that a topological space that admits a nontransitive totally bounded quasi-uniformity, admits at least
$$2^{2^{N_0 } } $$
nontransitive totally bounded quasi-uniformities. Furthermore we show that each infinite T
2-space admits at least
$$2^{2^{N_0 } } $$
transitive totally bounded quasi-uniformities. In fact, each supersober space having a discrete subspace of infinite cardinality κ admits at least
$$2^{2^k } $$
transitive totally bounded quasi-uniformities.
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