Geodesic
Spaces with star countable extent
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 3, pp. 381-395.

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For a topological property $P$, we say that a space $X$ is star $P$ if for every open cover $\mathcal{U}$ of the space $X$ there exists $A\subset X$ such that $st (A,\mathcal{U})= X$. We consider space with star countable extent establishing the relations between the star countable extent property and the properties star Lindelöf and feebly Lindelöf. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindelöf property or separability. An example is given of a Tychonoff star Lindelöf space with a point countable base which is not star countable.
DOI : 10.14712/1213-7243.2015.176
Classification : 54B05, 54B10, 54C10, 54D20
Keywords: extent; star properties; star countable spaces; star Lindelöf spaces; feebly Lindelöf spaces 
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Rojas-Sánchez, A. D.; Tamariz-Mascarúa, Á. Spaces with star countable extent. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 3, pp. 381-395. doi : 10.14712/1213-7243.2015.176. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.176/

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