# 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…

## References

SHOWING 1-10 OF 26 REFERENCES

Limited information strategies and discrete selectivity

- MathematicsTopology and its Applications
- 2019

We relate the property of discrete selectivity and its corresponding game, both recently introduced by V.V. Tkachuck, to a variety of selection principles and point picking games. In particular we…

Selective Games on Binary Relations

- Mathematics
- 2014

Abstract We present a unified approach, based on dominating families in binary relations, for the study of topological properties defined in terms of selection principles and the games associated to…

Combinatorics of open covers I: Ramsey theory

- Mathematics
- 1996

Abstract We study several schemas for generating from one sort of open cover of a topological space a second sort of open cover. Some of these schemas come from classical literature, others are…

Metrizable spaces where the inductive dimensions disagree

- Mathematics
- 1990

A method for constructing zero-dimensional metrizable spaces is given. Using generalizations of Roy's technique, these spaces can often be shown to have positive large inductive dimension. Examples…

Failure of equivalence of dimension concepts for metric spaces

- Mathematics
- 1962

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)…

Spaces whose n th power is weakly infinite-dimensional but whose (n+1) th power is not

- Mathematics
- 1993

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.

The Combinatorics of Open Covers

- Mathematics
- 1996

The combinatorics of open covers is a study of Cantor’s diagonal argument in various contexts. The field has its roots in a few basic selection principles that arose from the study of problems in…

Dual selection games

- Mathematics
- 2018

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 strategy for the opponent…

Relative dimension r-dim and finite spaces

- Mathematics
- 2013

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…

When does the Haver property imply selective screenability

- Mathematics
- 2007

We point out that in metric spaces Haver’s property is not equivalent to the property introduced by Addis and Gresham. We prove that they are equal when the space has the Hurewicz property. We prove…