On linearly Lindelöf and strongly discretely Lindelöf spaces

We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed 2^{\omega }, and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.

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Bibliographic Details
Published in:	Proceedings of the American Mathematical Society Vol. 127; no. 8; pp. 2449 - 2458
Main Authors:	Arhangel’skii, A. V., Buzyakova, R. Z.
Format:	Journal Article
Language:	English
Published:	American Mathematical Society 01-08-1999
Subjects:	Cardinal points Cardinality Compactification First countable General topology Mathematical theorems Mathematics Numbers Topological spaces Tychonoff spaces complete accumulation point Lindelöf space G_{2^{\omega }}$-set first countability free sequence linearly Lindelöf space
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Description
Summary:	We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed 2^{\omega }, and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.
ISSN:	0002-9939 1088-6826
DOI:	10.1090/S0002-9939-99-04783-8