• 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… 

References

SHOWING 1-10 OF 26 REFERENCES
Failure of equivalence of dimension concepts for metric spaces
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
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
Dual selection games
Relative dimension r-dim and finite spaces
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
Selection principles and countable dimension
We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.
...
1
2
3
...