Displaying similar documents to “Selection principles and Baire spaces”

A survey on topological games and their applications in analysis.

Jiling Cao, Warren B. Moors (2006)

RACSAM

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In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topics given here do not necessarily represent the most important problems from the area of topological games, but rather, they represent a selection of problems that are of interest to the authors.

A mixed duel under arbitrary motion and uncertain existence of the shot

Stanisław Trybuła (1993)

Applicationes Mathematicae

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The purpose of the paper is to solve a mixed duel in which the numbers of shots given to the players are independent 0-1-valued random variables. The players know their distributions as well as the accuracy function P, the same for both players. It is assumed that the players can move as they like and that the maximal speed of the first player is greater than that of the second player. It is shown that the game has a value, and a pair of optimal strategies is found.

The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.

Taras Banakh, Anatolij Plichko (2006)

RACSAM

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Answering a question of Halbeisen we prove (by two different methods) that the algebraic dimension of each infinite-dimensional complete linear metric space X equals the size of X. A topological method gives a bit more: the algebraic dimension of a linear metric space X equals |X| provided the hyperspace K(X) of compact subsets of X is a Baire space. Studying the interplay between Baire properties of a linear metric space X and its hyperspace, we construct a hereditarily Baire linear...