A first countable, initially \(\omega _1\)-compact but non-compact space (Q1030193)
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scientific article; zbMATH DE number 5573797
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A first countable, initially \(\omega _1\)-compact but non-compact space |
scientific article; zbMATH DE number 5573797 |
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A first countable, initially \(\omega _1\)-compact but non-compact space (English)
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1 July 2009
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It is known that under CH an initially \(\omega_1\)-compact \(T_3\) space of countable tightness is compact. In this paper, by forcing, the authors construct a locally compact, first countable, zero-dimensional, normal, initially \(\omega_1\)-compact, non-compact space \(X\) of cardinality \(\omega_2\). An interesting consequence is that the Alexandroff one-point compactification of \(X\) has no non-trivial converging \(\omega_1\)-sequences.
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initially \(\omega_1\)-compact
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locally compact
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forcing
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\(\Delta\)-function
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CH
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