Some properties related to [a,b]-compactness
Some propositions equivalent to the Sikorski Extension Theorem for Boolean algebras
Some Questions on Metrizability
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 Eberlein compacts
Some remarks on Michael's question concerning Cartesian products of Lindelöf spaces
Some remarks on preservation of topological products
Some remarks on the product of two -compact subsets
For a cardinal , we say that a subset of a space is -compact in if for every continuous function , is a compact subset of . If is a -compact subset of a space , then denotes the degree of -compactness of in . A space is called -pseudocompact if is -compact into itself. For each cardinal , we give an example of an -pseudocompact space such that 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
A space is truly weakly pseudocompact if 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 for every ; (2) every locally bounded space is truly weakly pseudocompact; (3) for , the -Lindelöfication of a discrete space of cardinality is weakly pseudocompact if .
Some results on expansions for normal and completely normal 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 sequentially compact extensions
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.
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 separation axioms in fuzzy topological spaces
Some set-theoretic constructions in topology
Some topological consequences of the Product Measure Extension Axiom