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Corpus ID: 238857035

On strategies for selection games related to countable dimension

@inproceedings{Caruvana2021OnSF,
title={On strategies for selection games related to countable dimension},
author={Christopher Caruvana and Steven Clontz},
year={2021}
}

Two selection games from the literature, Gc(O,O) and G1(Ozd,O), are known to characterize countable dimension among certain spaces. This paper studies their perfectand limitedinformation strategies, and investigates issues related to non-equivalent characterizations of zero-dimensionality for spaces that are not both separable and metrizable. To relate results on zero-dimensional and finite-dimensional spaces, a generalization of Telgársky’s proof that the point-open and finite-open games are… Expand

Introduction. The three classical set-theoretic concepts of dimensions for topological spaces are [2, p. 153]: small inductive dimension —denoted by ind—such that ind (5) = — 1 if S is empty, ind(S)… Expand

For every natural number n we construct a metrizable separable space Y such that yn is weakly infinite-dimensional (moreover, is a C-space) but yn+1 is strongly infinite-dimensional.

In a relative covering dimension is defined and studied which is denoted by r-dim. In this paper we give an algorithm of polynomial order for computing the dimension r-dim of a pair (Q,X), where Q is… Expand