Convergence in compacta and linear Lindelöfness
Arhangel'skii, Aleksander V. ; Buzyakova, Raushan Z.
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 159-166 / Harvested from Czech Digital Mathematics Library
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Let $X$ be a compact Hausdorff space with a point $x$ such that $X\setminus \{ x\}$ is linearly Lindelöf. Is then $X$ first countable at $x$? What if this is true for every $x$ in $X$? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is ``yes'' when $X$ is, in addition, $\omega $-monolithic. We also prove that if $X$ is compact, Hausdorff, and $X\setminus \{ x\}$ is strongly discretely Lindelöf, for every $x$ in $X$, then $X$ is first countable. An example of linearly Lindelöf hereditarily realcompact non-Lindelöf space is constructed. Some intriguing open problems are formulated.

Publié le : 1998-01-01
Classification:  54A25,  54D30,  54E35,  54F99 
@article{118994,
     author = {Aleksander V. Arhangel'skii and Raushan Z. Buzyakova},
     title = {Convergence in compacta and linear Lindel\"ofness},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {159-166},
     zbl = {0937.54022},
     mrnumber = {1623006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118994}
}

Arhangel'skii, Aleksander V.; Buzyakova, Raushan Z. Convergence in compacta and linear Lindelöfness. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 159-166. http://gdmltest.u-ga.fr/item/118994/

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