36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

"On set (strongly) star Menger"

Giacopello, Davide

Let ${\mathcal U}$ be a cover of a space $X$ and $A$ be a subset of $X$; the star of $A$ with respect to ${\mathcal U}$ is the set $st(A,{\mathcal U})=\bigcup\{U:U\in{\mathcal U}\;\hbox{and}\;U\cap A\neq\emptyset\}$. In this talk we consider some recent relative star versions of Menger property and the corresponding Hurewicz-type, called set (strongly) star Menger and set (strongly) star Hurewicz, introduced by Kocinac, Konca and Singh. We show that the set strongly star Menger and set strongly star Hurewicz are between countable compactness and the property of having countable extent. Also we study the behavior of all this properties with respect the product with a compact space. Among other things we answer to some recent questions posed by Kocinac, Konca and Singh. This is a joint work with M. Bonanzinga and F. Maesano

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