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Displaying 1541 – 1560 of 1977

Some properties of relatively strong pseudocompactness

Guo-Fang Zhang (2008)

Czechoslovak Mathematical Journal

In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space $X$ and a subspace $Y$ satisfy that $Y \subset \bar{Int Y}$ and $Y$ is strongly pseudocompact and metacompact in $X$ , then $Y$ is compact in $X$ . We also give an example to demonstrate that the condition $Y \subset \bar{Int Y}$ can not be omitted.

Some properties of subsets, almost closed mappings and paracompactness.

Kovačević, Ilija (1999)

Novi Sad Journal of Mathematics

Some properties of the remainder of Stone-Čech compactifications

Takesi Isiwata (1974)

Fundamenta Mathematicae

Some Properties of the Sorgenfrey Line and the Sorgenfrey Plane

Adam St. Arnaud, Piotr Rudnicki (2013)

Formalized Mathematics

We first provide a modified version of the proof in [3] that the Sorgenfrey line is T1. Here, we prove that it is in fact T2, a stronger result. Next, we prove that all subspaces of ℝ1 (that is the real line with the usual topology) are Lindel¨of. We utilize this result in the proof that the Sorgenfrey line is Lindel¨of, which is based on the proof found in [8]. Next, we construct the Sorgenfrey plane, as the product topology of the Sorgenfrey line and itself. We prove that the Sorgenfrey plane...

Some properties related to [a,b]-compactness

J. Vaughan (1975)

Fundamenta Mathematicae

Some propositions equivalent to the Sikorski Extension Theorem for Boolean algebras

J. Bell (1988)

Fundamenta Mathematicae

Some Questions on Metrizability

Ying Ge, Jian-Hua Shen (2004)

Publications de l'Institut Mathématique

Some relative topological properties

Lj. D. Kočinac (1992)

Matematički Vesnik

Some remarks about bijections onto metric spaces

Alexander P. Shostak (1984)

Czechoslovak Mathematical Journal

Some remarks on almost Lindel{ö}f spaces and weakly Lindel{ö}f spaces

Yan-Kui Song, Yun-Yun Zhang (2010)

Matematički Vesnik

Some remarks on Eberlein compacts

K. Alster (1979)

Fundamenta Mathematicae

Some remarks on Michael's question concerning Cartesian products of Lindelöf spaces

K. Alster (1982)

Colloquium Mathematicae

Some remarks on preservation of topological products

Luciano Stramaccia (1989)

Commentationes Mathematicae Universitatis Carolinae

Some remarks on the product of two $C_{α}$ -compact subsets

Salvador García-Ferreira, Manuel Sanchis, Stephen W. Watson (2000)

Czechoslovak Mathematical Journal

For a cardinal $α$ , we say that a subset $B$ of a space $X$ is $C_{α}$ -compact in $X$ if for every continuous function $f X \to ℝ^{α}$ , $f [B]$ is a compact subset of $ℝ^{α}$ . If $B$ is a $C$ -compact subset of a space $X$ , then $ρ (B, X)$ denotes the degree of $C_{α}$ -compactness of $B$ in $X$ . A space $X$ is called $α$ -pseudocompact if $X$ is $C_{α}$ -compact into itself. For each cardinal $α$ , we give an example of an $α$ -pseudocompact space $X$ such that $X \times X$ is not pseudocompact: this answers a question posed by T. Retta in “Some cardinal generalizations of pseudocompactness”...

Some results and problems about weakly pseudocompact spaces

Oleg Okunev, Angel Tamariz-Mascarúa (2000)

Commentationes Mathematicae Universitatis Carolinae

A space $X$ is truly weakly pseudocompact if $X$ is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with $χ (x, X) > ω$ for every $x \in X$ ; (2) every locally bounded space is truly weakly pseudocompact; (3) for $ω < κ < α$ , the $κ$ -Lindelöfication of a discrete space of cardinality $α$ is weakly pseudocompact if $κ = κ^{ω}$ .

Some results on expansions for normal and completely normal spaces.

Mary Powderly (1974)

Journal für die reine und angewandte Mathematik

Some results on $L Σ (κ)$ -spaces

Fidel Casarrubias Segura, Oleg Okunev, Paniagua C. G. Ramírez (2008)

Commentationes Mathematicae Universitatis Carolinae

We present several results related to $L Σ (κ)$ -spaces where $κ$ is a finite cardinal or $ω$ ; we consider products and some constructions that lead from spaces of these classes to other spaces of similar classes.

Some results on $[n, m]$ -paracompact and $[n, m]$ -compact spaces.

Hdeib, Hasan Z., Ünlü, Yusuf (1997)

International Journal of Mathematics and Mathematical Sciences

Some results on semi-stratifiable spaces

Wei-Feng Xuan, Yan-Kui Song (2019)

Mathematica Bohemica

We study relationships between separability with other properties in semi-stratifiable spaces. Especially, we prove the following statements: (1) If $X$ is a semi-stratifiable space, then $X$ is separable if and only if $X$ is $D C (ω_{1})$ ; (2) If $X$ is a star countable extent semi-stratifiable space and has a dense metrizable subspace, then $X$ is separable; (3) Let $X$ be a $ω$ -monolithic star countable extent semi-stratifiable space. If $t (X) = ω$ and $d (X) \leq ω_{1}$ , then $X$ is hereditarily separable. Finally, we prove that for any $T_{1}$ -space...

Some results on sequentially compact extensions

Maria Cristina Vipera (1998)

Commentationes Mathematicae Universitatis Carolinae

The class of Hausdorff spaces (or of Tychonoff spaces) which admit a Hausdorff (respectively Tychonoff) sequentially compact extension has not been characterized. We give some new conditions, in particular, we prove that every Tychonoff locally sequentially compact space has a Tychonoff one-point sequentially compact extension. We also give some results about extension of functions and about lattice properties of the family of all minimal sequentially compact extensions of a given space.

Currently displaying 1541 – 1560 of 1977

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