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We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of $𝒫 (ω)$ with the Cantor set topology.

Some problems and lines of investigation in general topology

Aleksander V. Arhangel'skii (1988)

Commentationes Mathematicae Universitatis Carolinae

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 related to [a,b]-compactness

J. Vaughan (1975)

Fundamenta Mathematicae

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 Michael's question concerning Cartesian products of Lindelöf spaces

K. Alster (1982)

Colloquium Mathematicae

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 spaces with $ℵ_{1}$ -calibre

Wei-Feng Xuan, Wei-Xue Shi (2016)

Commentationes Mathematicae Universitatis Carolinae

We prove that, assuming CH, if $X$ is a space with $ℵ_{1}$ -calibre and a zeroset diagonal, then $X$ is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular $G_{δ}$ -diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. We also make some observations on spaces with $ℵ_{1}$ -calibre.

Some topological properties weaker than Lindelofness

Yan-Kui Song (2008)

Matematički Vesnik

Some versions of relative paracompactness and their absolute embeddings

Shinji Kawaguchi (2007)

Commentationes Mathematicae Universitatis Carolinae

Arhangel’skii [Sci. Math. Jpn. 55 (2002), 153–201] defined notions of relative paracompactness in terms of locally finite open partial refinement and asked if one can generalize the notions above to the well known Michael’s criteria of paracompactness in [17] and [18]. In this paper, we consider some versions of relative paracompactness defined by locally finite (not necessarily open) partial refinement or locally finite closed partial refinement, and also consider closure-preserving cases, such...

Some weak covering properties and infinite games

Masami Sakai (2014)

Open Mathematics

We show that (I) there is a Lindelöf space which is not weakly Menger, (II) there is a Menger space for which TWO does not have a winning strategy in the game Gfin(O,Do). These affirmatively answer questions posed in Babinkostova, Pansera and Scheepers [Babinkostova L., Pansera B.A., Scheepers M., Weak covering properties and infinite games, Topology Appl., 2012, 159(17), 3644–3657]. The result (I) automatically gives an affirmative answer of Wingers’ problem [Wingers L., Box products and Hurewicz...

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