## 16 Citations

PRODUCTS AND SELECTION PRINCIPLES

- Mathematics, Economics
- 2007

We study when the product of separable metric spaces has the selective screenability property, the Menger property, or the Rothberger property. Our results imply the product of a Lusin set and (1) a…

A METRIC SPACE WITH THE HAVER PROPERTY WHOSE SQUARE FAILS THIS PROPERTY

- Mathematics
- 2008

Haver introduced the following property of metric spaces (X, d): for each sequence 1, 2, . . . of positive numbers there exist collections V1,V2, . . . of open subsets of X, the union ⋃ i Vi of which…

A metric space with the Haver property whose square fails this property

- Mathematics
- 2008

Haver introduced the following property of metric spaces (X,d): for each sequence ∈ 1 ,∈ 2 ;.. of positive numbers there exist collections ν 1 , ν 2 ,. of open subsets of X, the union ∪ i ν i of…

Selective Screenability and the Hurewicz Property

- Mathematics, Economics
- 2008

We characterize the Hurewicz covering property in metrizable spaces in terms of properties of the metrics of the space. Then we show that a weak version of selective screenability, when combined with…

Selective Strong Screenability

- Mathematics
- 2018

It is found that a great deal of the proofs about selective screenability readily carry over to proofs for the analogous version for selective strong screenability.

Selection Principles and Baire spaces

- Mathematics
- 2007

We prove that if X is a separable metric space with the Hurewicz covering property, then the Banach-Mazur game played on X is determined. The implication is not true when "Hurewicz covering property"…

## References

SHOWING 1-10 OF 13 REFERENCES

Finite Powers of Strong Measure Zero Sets

- MathematicsJ. Symb. Log.
- 1999

2 and 3 yield characterizations of strong measure zeroness for a-totally bounded metric spaces in terms of Ramseyan theorems in the more general context of metric spaces.

Products of infinite-dimensional spaces

- Mathematics
- 1990

Observations concerning the product of R. Pol's weakly infinitedimensional uncountable-dimensional compactum with various spaces are made. A proof showing that the product of a C-space and a compact…

A weakly infinite-dimensional compactum which is not countable-dimensional

- Mathematics
- 1981

A compact metric space is constructed which is neither a countable union of zero-dimensional sets nor has an essential map onto the Hilbert cube. We consider only separable metrizable spaces and a…

Metrization of Topological Spaces

- MathematicsCanadian Journal of Mathematics
- 1951

A single valued function D(x, y) is a metric for a topological space provided that for points x, y, z of the space: 1. D(x, y) ≽ 0, the equality holding if and only if x = y, 2. D(x, y) = D(y, x)…

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.

Selective versions of screenability

- Mathematics
- 2001

In this paper 1 we introduce a new selection principle for topological spaces and consider its connection with the classical selection principles.

Selection principles and countable dimension

- Mathematics
- 2007

We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.

Closed pre-images of C-spaces

- Mathematica Japonica 34
- 1989