PRODUCTS AND SELECTION PRINCIPLES
- Mathematics, Economics
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
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
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
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
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
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"…
SHOWING 1-10 OF 13 REFERENCES
Finite Powers of Strong Measure Zero Sets
- MathematicsJ. Symb. Log.
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
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
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
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
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
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
We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.
Closed pre-images of C-spaces
- Mathematica Japonica 34