a $\gamma$-cover if $\mathcal{U}$ is infinite, and each infinite subset of $\mathcal{U}$ still covers the space. The symbol $\Gamma$ denotes the collection of open $\gamma$ covers of a space. In [@GN] Gerlits and Nagy introduced the notion of a $\gamma$-space: A topological space which satisfies the selection principle ${{\sf S}_1}(\Omega,\Gamma)$ is said to be a $\gamma$-*space*. It is evident that each $\gamma$-space is a Rothberger space. In Theorem 1 of [@GN] the authors prove

For a ${\sf T}_{3\frac{1}{2}}$-space TWO has a winning strategy in ${{\sf G}_1}({\mathcal{O}},{\mathcal{O}})$ if, and only if, TWO has a winning strategy in ${{\sf G}_1}(\Omega,\Gamma)$.

It is also evident that if TWO has a winning strategy in the game ${{\sf G}_1}(\Omega,\Gamma)$, then the underlying space is a $\gamma$-space.

\[GNcorollary\] For each uncountable cardinal number $\kappa$ there is a Lindelöf $P$-group of cardinality $\kappa$ on which TWO has a winning strategy in the game ${{\sf G}_1}(\Omega,\Gamma)$.

By a result of Gerlits and Nagy if TWO has a winning strategy in ${{\sf G}_1}({\mathcal{O}},{\mathcal{O}})$, then TWO has a winning strategy in ${{\sf G}_1}(\Omega,\Gamma)$. $\Box$

Large $\sigma$-compact Rothberger bounded ${\sf T}_0$ groups.
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In Proposition 4 of [@Corson], Corson proves essentially the following theorem[^4]:

\[Corson\] Let $\{X_i:i\in I\}$ be a family 