Geodesic
Some observations on the mildly Menger property and topological games
Filomat, Tome 36 (2022) no. 15, p. 5289

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

In this paper, we defined two new games-the mildly Menger game and the compact-clopen game. In a zero-dimensional space, the Menger game is equivalent to the mildly Menger game and the compact-open game is equivalent to the compact-clopen game. An example is given for a space on which the mildly Menger game is undetermined. Also we introduced a new game namely K-quasi-component-clopen game and proved that this game is equivalent to the compact-clopen game. Then we proved that if a topological space is a union of countably many quasi-components of compact sets, then TWO has a winning strategy in the mildly Menger game.
DOI : 10.2298/FIL2215289B
Classification : 54D20, 54A20, 91A44
Keywords: Selection principles, compact-clopen game, zero-dimensional space, K -quasi-component-clopen game, Menger space, Menger game, mildly Menger space, mildly Menger game 
Manoj Bhardwaj; Alexander V Osipov. Some observations on the mildly Menger property and topological games. Filomat, Tome 36 (2022) no. 15, p. 5289 . doi: 10.2298/FIL2215289B
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     title = {Some observations on the mildly {Menger} property and topological games},
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