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On Typical Compact Convex Sets in Hilbert Spaces

De Blasi, F. (1997)

Serdica Mathematical Journal

Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.

On uncountable unions and intersections of measurable sets.

Balcerzak, M., Kharazishvili, A. (1999)

Georgian Mathematical Journal

On β-favorability of the strong Choquet game

László Zsilinszky (2011)

Colloquium Mathematicae

In the main result, partially answering a question of Telgársky, the following is proven: if X is a first countable R₀-space, then player β (i.e. the EMPTY player) has a winning strategy in the strong Choquet game on X if and only if X contains a nonempty $W_{δ}$ -subspace which is of the first category in itself.

On $ω$ -resolvable and almost- $ω$ -resolvable spaces

J. Angoa, M. Ibarra, Angel Tamariz-Mascarúa (2008)

Commentationes Mathematicae Universitatis Carolinae

We continue the study of almost- $ω$ -resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, Spaces of continuous functions, box products and almost- $ω$ -resoluble spaces, Comment. Math. Univ. Carolin. 43 (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded $T_{0}$ space with countable tightness and every $T_{1}$ space with $π$ -weight $\leq ℵ_{1}$ is hereditarily almost- $ω$ -resolvable, (2) every crowded paracompact $T_{2}$ space which is the closed preimage of a crowded Fréchet $T_{2}$ space in such a way that the...

Ordered Cauchy spaces.

Kent, Darrell C., Vainio, R. (1985)

International Journal of Mathematics and Mathematical Sciences