Abstract: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 Lindel\"of and feebly Lindel\"of. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindel\"of property or separability. An example is given of a Tychonoff star Lindel\"of space with a point countable base which is not star countable.
Keywords: extent; star properties; star countable spaces; star Lindel\"of spaces; feebly Lindel\"of spaces
DOI: DOI 10.14712/1213-7243.2015.176
AMS Subject Classification: 54D20 54C10 54B10 54B05