9 papers · 1 filter
On Traditional Menger and Rothberger Variations
Christopher Caruvana, Steven Clontz, Jared Holshouser
We present a comprehensive report on the relationships between variations of the Menger and Rothberger selection properties with respect to -covers and -covers in the most ge…
Non-Hausdorff Properties
Steven Clontz
Several weakenings of the property for topological spaces, including -Hausdorff, , weakly Hausdorff, semi-Hausdorff, , and , have been studied by mathematician…
Metrizability of Mahavier products indexed by partial orders
Steven Clontz, Jacob Dunham
Let be separable metrizable, and let be a non-trivial relation on . For a given partial order , the Mahavier product (also…
Arhangelskii's -principles and selection games
Steven Clontz
Arhangelskii's properties and defined for convergent sequences may be characterized in terms of Scheeper's selection principles. We generalize these results to hold for…
On Ramsey properties, function spaces, and topological games
Steven Clontz, Alexander V. Osipov
An open question of Gruenhage asks if all strategically selectively separable spaces are Markov selectively separable, a game-theoretic statement known to hold for countable spaces…
Dual Selection Games
Steven Clontz
Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strateg…