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A note on D-spaces

Shou Lin (2006)

Commentationes Mathematicae Universitatis Carolinae

Every semi-stratifiable space or strong Σ -space has a σ -cushioned (mod k )-network. In this paper it is showed that every space with a σ -cushioned (mod k )-network is a D-space, which is a common generalization of some results about D-spaces.

Cartesian closed hull for (quasi-)metric spaces (revisited)

Mark Nauwelaerts (2000)

Commentationes Mathematicae Universitatis Carolinae

An existing description of the cartesian closed topological hull of p MET ∞ , the category of extended pseudo-metric spaces and nonexpansive maps, is simplified, and as a result, this hull is shown to be a special instance of a “family” of cartesian closed topological subconstructs of p q s MET ∞ , the category of extended pseudo-quasi-semi-metric spaces (also known as quasi-distance spaces) and nonexpansive maps. Furthermore, another special instance of this family yields the cartesian closed topological hull of...

Diagonal conditions in ordered spaces

Harold Bennett, David Lutzer (1997)

Fundamenta Mathematicae

For a space X and a regular uncountable cardinal κ ≤ |X| we say that κ ∈ D(X) if for each T ⊂ X 2 - Δ ( X ) with |T| = κ, there is an open neighborhood W of Δ(X) such that |T - W| = κ. If ω 1 ∈ D ( X ) then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization theorems...

Functional characterizations of p-spaces

Ľubica Holá (2013)

Open Mathematics

We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.

Mapping theorems on ℵ -spaces

Masami Sakai (2008)

Commentationes Mathematicae Universitatis Carolinae

In this paper we improve some mapping theorems on ℵ -spaces. For instance we show that an ℵ -space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an ℵ -space is preserved by a closed and open map.

Notes on c f p -covers

Shou Lin, Peng Fei Yan (2003)

Commentationes Mathematicae Universitatis Carolinae

The main purpose of this paper is to establish general conditions under which T 2 -spaces are compact-covering images of metric spaces by using the concept of c f p -covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of g -metrizable spaces by compact-covering σ -maps and m s s c -maps.

On spaces with point-countable k -systems

Iwao Yoshioka (2004)

Commentationes Mathematicae Universitatis Carolinae

This paper deals with the behavior of M -spaces, countably bi-quasi- k -spaces and singly bi-quasi- k -spaces with point-countable k -systems. For example, we show that every M -space with a point-countable k -system is locally compact paracompact, and every separable singly bi-quasi- k -space with a point-countable k -system has a countable k -system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael’s paper [15] when the spaces have point-countable k -systems.

On subsets of Alexandroff duplicates

Takemi Mizokami (2005)

Commentationes Mathematicae Universitatis Carolinae

We characterize the subsets of the Alexandroff duplicate which have a G δ -diagonal and the subsets which are M-spaces in the sense of Morita.

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