La completion universelle d'un espace metrique.
La complétion universelle d'un produit d'espaces complètement réguliers
Large families of dense pseudocompact subgroups of compact groups
We prove that every nonmetrizable compact connected Abelian group G has a family H of size |G|, the maximal size possible, consisting of proper dense pseudocompact subgroups of G such that H ∩ H'={0} for distinct H,H' ∈ H. An easy example shows that connectedness of G is essential in the above result. In the general case we establish that every nonmetrizable compact Abelian group G has a family H of size |G| consisting of proper dense pseudocompact subgroups of G such that each intersection H H'...
Lebesgue measurability of separately continuous functions and separability.
Local compactness in approach spaces. II.
Mappings on -paracompact spaces.
Maximal pseudocompact spaces and the Preiss-Simon property
We study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact space is maximal pseudocompact. If X is hereditarily maximal pseudocompact then X × Y is hereditarily maximal pseudocompact for any first countable compact space Y. It turns out that hereditary maximal pseudocompactness coincides with the Preiss-Simon property in countably compact spaces. In compact spaces, hereditary MP-property is invariant under...
Mazur-like topological linear spaces and their products
Topological linear spaces having the property that some sequentially continuous linear maps on them are continuous, are investigated. It is shown that such properties (and close ones, e.g., bornological-like properties) are closed under large products.
Monotonically normal -separable spaces may not be perfect
A topological space is said to be -separable if has a -closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that -separable PIGO spaces are perfect and asked if -separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of -separable monotonically normal spaces which are not perfect. Extremely normal -separable spaces are shown to be stratifiable.
More Lusin properties in the product space
More on strongly sequential spaces
Strongly sequential spaces were introduced and studied to solve a problem of Tanaka concerning the product of sequential topologies. In this paper, further properties of strongly sequential spaces are investigated.
More on the product of pseudo radial spaces
It is proved that the product of two pseudo radial compact spaces is pseudo radial provided that one of them is monolithic.
More on -Ohio completeness
We study closed subspaces of -Ohio complete spaces and, for uncountable cardinal, we prove a characterization for them. We then investigate the behaviour of products of -Ohio complete spaces. We prove that, if the cardinal is endowed with either the order or the discrete topology, the space is not -Ohio complete. As a consequence, we show that, if is less than the first weakly inaccessible cardinal, then neither the space , nor the space is -Ohio complete.
Narrow spaces, products of topological spaces and supertiny sequences of A. Szymański
No hedgehog in the product?
Assuming OCA, we shall prove that for some pairs of Fréchet -spaces , the Fréchetness of the product implies that is . Assuming MA, we shall construct a pair of spaces satisfying the assumptions of the theorem.
Non standard metric products.
Non-meager P-filters are countable dense homogeneous
We prove that if ℱ is a non-meager P-filter, then both ℱ and are countable dense homogeneous spaces.
Normal subspaces in products of two ordinals
Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of .
Normality and Martin's axiom
Normality and paracompactness in finite and countable Cartesian products