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Relatively realcompact sets and nearly pseudocompact spaces

John J. Schommer (1993)

Commentationes Mathematicae Universitatis Carolinae

A space is said to be nearly pseudocompact iff v X - X is dense in β X - X . In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.

Relaxation theorem for set-valued functions with decomposable values

Andrzej Kisielewicz (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has f χ A + g χ T K . Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.

Remark on the Abstract Dirichlet Problem for Baire-One Functions

Ondřej F. K. Kalenda (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine Baire-one function....

Remarks on extremally disconnected semitopological groups

Igor V. Protasov (2002)

Commentationes Mathematicae Universitatis Carolinae

Answering recent question of A.V. Arhangel'skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.

Remarks on L B I -subalgebras of C ( X )

Mehdi Parsinia (2016)

Commentationes Mathematicae Universitatis Carolinae

Let A ( X ) denote a subalgebra of C ( X ) which is closed under local bounded inversion, briefly, an L B I -subalgebra. These subalgebras were first introduced and studied in Redlin L., Watson S., Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151–163. By characterizing maximal ideals of A ( X ) , we generalize the notion of z A β -ideals, which was first introduced in Acharyya S.K., De D., An interesting class of ideals in subalgebras of C ( X ) containing...

Remarks on sequence-covering maps

Luong Quoc Tuyen (2012)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we prove that each sequence-covering and boundary-compact map on g -metrizable spaces is 1-sequence-covering. Then, we give some relationships between sequence-covering maps and 1-sequence-covering maps or weak-open maps, and give an affirmative answer to the problem posed by F.C. Lin and S. Lin in [Lin.F.C.and.Lin.S-2011].

Remarks on strongly star-Menger spaces

Yan-Kui Song (2013)

Commentationes Mathematicae Universitatis Carolinae

A space X is strongly star-Menger if for each sequence ( 𝒰 n : n ) of open covers of X , there exists a sequence ( K n : n N ) of finite subsets of X such that { S t ( K n , 𝒰 n ) : n } is an open cover of X . In this paper, we investigate the relationship between strongly star-Menger spaces and related spaces, and also study topological properties of strongly star-Menger spaces.

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