Caliber (, ω) is not productive
Cardinal invariants of paratopological groups
We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf...
Cartesian products of -spaces.
Chain conditions and products
Characterizations of the countable infinite product of rationals and some related problems
Clone properties of topological spaces
Clone properties are the properties expressible by the first order sentence of the clone language. The present paper is a contribution to the field of problems asking when distinct sentences of the language determine distinct topological properties. We fully clarify the relations among the rigidity, the fix-point property, the image-determining property and the coconnectedness.
Closed embeddings into complements of -products
In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a -subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin axiom and...
Closed mapping theorems on -spaces with point-countable -networks
We prove some closed mapping theorems on -spaces with point-countable -networks. One of them generalizes Lašnev’s theorem. We also construct an example of a Hausdorff space with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a -space with a point-countable -network admitting a closed surjection which is not compact-covering contains a closed copy of .
Collectionwise Hausdorff property in product spaces
Compact spaces that do not map onto finite products
We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.
Compact-covering numbers
Compactness of Powers of ω
We characterize exactly the compactness properties of the product of κ copies of the space ω with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard elements in elementary extensions. We also have results involving products of possibly uncountable regular cardinals.
Compactness type properties in topological groups
Completely regular modification and products
Concerning products of proximally fine uniform spaces
Condensations of Cartesian products
We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space there is a such that can be condensed onto a normal (-compact) space if and only if there is no measurable cardinal. For any Tychonoff space and any cardinal there is a Tychonoff space which preserves many properties of and such that any one-to-one continuous image of , , contains a closed copy...
Connectivity properties in hyperspaces and product spaces
Continua whose hyperspace is a product
Continuous functions on products of topological spaces
Corrections to: “Remarks on subsets of Cartesian products of metric spaces”