EuDML | Browse

Displaying 21 – 27 of 27

Stationary and convergent strategies in Choquet games

François G. Dorais, Carl Mummert (2010)

Fundamenta Mathematicae

If Nonempty has a winning strategy against Empty in the Choquet game on a space, the space is said to be a Choquet space. Such a winning strategy allows Nonempty to consider the entire finite history of previous moves before making each new move; a stationary strategy only permits Nonempty to consider the previous move by Empty. We show that Nonempty has a stationary winning strategy for every second-countable T₁ Choquet space. More generally, Nonempty has a stationary winning strategy for...

The Dugundji extension property can fail in ωµ -metrizable spaces

Ian Stares, Jerry Vaughan (1996)

Fundamenta Mathematicae

We show that there exist $ω_{μ}$ -metrizable spaces which do not have the Dugundji extension property ( $2^{ω_{1}}$ with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.

Tychonoff products of super second countable and super separable metric spaces

Horst Herrlich, Kyriakos Keremedis, Eleftherios Tachtsis (2008)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Universal rational spaces [Book]

J. C. Mayer, E. D. Tymchatyn (1990)

Upper semicontinuous decompositions of spaces having bases of countable order

Worrell, J.M. jr. (1967)

Portugaliae mathematica

Weak-bases and $D$ -spaces

Dennis K. Burke (2007)

Commentationes Mathematicae Universitatis Carolinae

It is shown that certain weak-base structures on a topological space give a $D$ -space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are $D$ -spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Theorem.Any symmetrizable space $X$ is a $D$ -space $($ hereditarily $)$ . Hence, quotient mappings, with compact fibers, from metric spaces have a $D$ -space image. What about quotient $s$ -mappings? Arhangel’skii and Buzyakova have shown that...

Пространства с базами конечного ранга

А.В. Архангельский, В.В. Филиппов (1972)

Matematiceskij sbornik