Some cover properties of nonseparable metric spaces
Some covering spaces and types of compactness.
Some Generalizations of Lindelöf and Paracompact Spaces.
Some nowhere densely generated topological properties
Some observations on filters with properties defined by open covers
We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of with the Cantor set topology.
Some problems and lines of investigation in general topology
Some properties of relatively strong pseudocompactness
In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space and a subspace satisfy that and is strongly pseudocompact and metacompact in , then is compact in . We also give an example to demonstrate that the condition can not be omitted.
Some properties of subsets, almost closed mappings and paracompactness.
Some properties related to [a,b]-compactness
Some relative topological properties
Some remarks about bijections onto metric spaces
Some remarks on almost Lindel{ö}f spaces and weakly Lindel{ö}f spaces
Some remarks on Michael's question concerning Cartesian products of Lindelöf spaces
Some results on -spaces
We present several results related to -spaces where is a finite cardinal or ; we consider products and some constructions that lead from spaces of these classes to other spaces of similar classes.
Some results on -paracompact and -compact spaces.
Some results on semi-stratifiable spaces
We study relationships between separability with other properties in semi-stratifiable spaces. Especially, we prove the following statements: (1) If is a semi-stratifiable space, then is separable if and only if is ; (2) If is a star countable extent semi-stratifiable space and has a dense metrizable subspace, then is separable; (3) Let be a -monolithic star countable extent semi-stratifiable space. If and , then is hereditarily separable. Finally, we prove that for any -space...
Some results on spaces with -calibre
We prove that, assuming CH, if is a space with -calibre and a zeroset diagonal, then is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular -diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. We also make some observations on spaces with -calibre.
Some topological properties weaker than Lindelofness
Some versions of relative paracompactness and their absolute embeddings
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
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...