Some star and strongly star selection principles (Q1738974)

Connections between star-Menger and strongly star-Menger are explored. For example with a specified topology, $2^{\omega_1}$ is a metacompact regular space that is not strongly star-Menger but, with $\mathfrak d>\omega_1$, is star-Menger. Rudin's $\clubsuit$ example of a hereditarily separable, first countable de Caux-type space is Dowker and strongly star-Rothberger. If $X=Y\cup Z$ where $Y\cap Z=\varnothing$ such that $X$ is strongly star-Lindelöf, $Y$ closed discrete and $Z$ is $\sigma$-compact, then $X$ is strongly star-Menger (resp., strongly star-Hurewicz) if and only if $|Y|<\mathfrak d$ (resp., $<\mathfrak b$) and if $X$ is strongly star-Menger then the first player does not have a winning strategy in Kočinac's SSM game.