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- W2013668501 abstract "Let S denote a finite set of cardinal n. The discrete topology on S contains 2n open sets; the indiscrete topology contains 2 open sets. A partial answer is given to the question: For which intermediate integers m is there a topology on S with cardinal m? It is shown that no topology, other than the discrete, has cardinal greater than 3/4 2n. Other bounds are derived on the cardinality of connected, non-T0, connected and non-T0, and non-connected topologies. Proofs involve results in the theory of transitive digraphs." @default.
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- W2013668501 date "1968-07-01" @default.
- W2013668501 modified "2023-09-23" @default.
- W2013668501 title "Cardinality of finite topologies" @default.
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- W2013668501 doi "https://doi.org/10.1016/s0021-9800(68)80031-6" @default.
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