Baire generalized topological spaces, generalized metric spaces and infinite games
Different generalizations of topological Baire spaces to the case of generalized topological spaces are considered and the properties of such spaces are examined. In particular, these considerations are focused on the relationship between Baire generalized topological spaces and semi-continuous real functions and infinite games. The notion of generalized metric spaces corresponding to generalized topological spaces is introduced as an important tool in this discussion.
Key words and phrasesgeneralized topological space Baire property semi-continuous function generalized metric space set valued function Banach–Mazur game set function game
Mathematics Subject Classification54A05 54C30 91A05 91A06 54C60
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