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- W2102465305 abstract "Recent papers of Sharp [4] and Stephen [5] have shown that any finite topology with n points which is not discrete contains ⩽(34)2n open sets, and that this inequality is best possible. We use the correspondence between finite T0-topologies and partial orders to find all non-homeomorphic topologies with n points and ⩾(716)2n open sets. We determine which of these topologies are T0, and in the opposite direction we find finite T0 and non-T0 topologies with a small number of open sets. The corresponding results for topologies on a finite set are also given." @default.
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- W2102465305 date "1971-01-01" @default.
- W2102465305 modified "2023-09-23" @default.
- W2102465305 title "On the number of open sets of finite topologies" @default.
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- W2102465305 doi "https://doi.org/10.1016/0097-3165(71)90065-3" @default.
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