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- W2086084180 abstract "It is now well known that first countable compact Hausdorff spaces are either countable or have cardinality $c$. The situation for first countable $H$-closed spaces is that they have cardinality less than or equal $c$, and it is at least consistent that they may have cardinality ${aleph _1} < c$. We show that the situation is quite different for first countable $R$-closed spaces. We begin by constructing an example which has cardinality ${aleph _1}$. Let ${lambda _0}$ be the smallest cardinal greater than $c$ which is not a successor. For each cardinal $kappa$ with $c leqslant kappa leqslant {lambda _0}$ we construct a first countable $R$-closed space of cardinality $kappa$. We also construct a first countable $R$-closed space of cardinality $lambda _0^omega$. This seems to indicate that there is no reasonable upper bound to the cardinalities of $R$-closed spaces as a function of their character." @default.
- W2086084180 created "2016-06-24" @default.
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- W2086084180 date "1983-03-01" @default.
- W2086084180 modified "2023-09-25" @default.
- W2086084180 title "Cardinalities of first countable $R$-closed spaces" @default.
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- W2086084180 doi "https://doi.org/10.1090/s0002-9939-1983-0715880-x" @default.
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