Page 1 Next

Displaying 1 – 20 of 35

Showing per page

A note on transitively D -spaces

Liang-Xue Peng (2011)

Czechoslovak Mathematical Journal

In this note, we show that if for any transitive neighborhood assignment φ for X there is a point-countable refinement such that for any non-closed subset A of X there is some V such that | V A | ω , then X is transitively D . As a corollary, if X is a sequential space and has a point-countable w c s * -network then X is transitively D , and hence if X is a Hausdorff k -space and has a point-countable k -network, then X is transitively D . We prove that if X is a countably compact sequential space and has a point-countable...

Addition theorems, D -spaces and dually discrete spaces

Ofelia Teresa Alas, Vladimir Vladimirovich Tkachuk, Richard Gordon Wilson (2009)

Commentationes Mathematicae Universitatis Carolinae

A neighbourhood assignment in a space X is a family 𝒪 = { O x : x X } of open subsets of X such that x O x for any x X . A set Y X is a kernel of 𝒪 if 𝒪 ( Y ) = { O x : x Y } = X . If every neighbourhood assignment in X has a closed and discrete (respectively, discrete) kernel, then X is said to be a D -space (respectively a dually discrete space). In this paper we show among other things that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf P -space is a D -space and we prove an addition...

Algebras and spaces of dense constancies

Angelo Bella, Jorge Martinez, Scott D. Woodward (2001)

Czechoslovak Mathematical Journal

A DC-space (or space of dense constancies) is a Tychonoff space X such that for each f C ( X ) there is a family of open sets { U i i I } , the union of which is dense in X , such that f , restricted to each U i , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean f -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions...

Continuous pseudo-hairy spaces and continuous pseudo-fans

Janusz R. Prajs (2002)

Fundamenta Mathematicae

A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction r : X ̃ o n t o X such that all fibers r - 1 ( x ) are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum Y X is called a continuous pseudo-fan of a compactum X if there are a point c Y X and a family ℱ of pseudo-arcs such that = Y X , any subcontinuum of Y X intersecting two different elements of ℱ contains c, and ℱ is homeomorphic to X (with...

More than a 0-point

Jana Flašková (2006)

Commentationes Mathematicae Universitatis Carolinae

We construct in ZFC an ultrafilter U * such that for every one-to-one function f : there exists U U with f [ U ] in the summable ideal, i.e. the sum of reciprocals of its elements converges. This strengthens Gryzlov’s result concerning the existence of 0 -points.

On the k -Baire property

Alessandro Fedeli (1993)

Commentationes Mathematicae Universitatis Carolinae

In this note we show the following theorem: “Let X be an almost k -discrete space, where k is a regular cardinal. Then X is k + -Baire iff it is a k -Baire space and every point- k open cover 𝒰 of X such that card ( 𝒰 ) k is locally- k at a dense set of points.” For k = 0 we obtain a well-known characterization of Baire spaces. The case k = 1 is also discussed.

On weakly monotonically monolithic spaces

Liang-Xue Peng (2010)

Commentationes Mathematicae Universitatis Carolinae

In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a D -space. Thus most known conclusions on D -spaces can be obtained by this conclusion. As a corollary, we have that if a regular space X is sequential and has a point-countable w c s * -network then X is a D -space.

Radon-Nikodým compact spaces of low weight and Banach spaces

Antonio Avilés (2005)

Studia Mathematica

We prove that a continuous image of a Radon-Nikodým compact of weight less than b is Radon-Nikodým compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than b are Asplund generated. In this case, in addition, there exists a subspace of an Asplund generated space which is not Asplund generated and which has density character exactly b.

Currently displaying 1 – 20 of 35

Page 1 Next