On proximity ordered spaces
On some spaces which are covered by a product space
In this note, a topological version of the results obtained, in connection with the de Rham reducibility theorem (Comment. Math. Helv., 26 ( 1952), 328–344), by S. Kashiwabara (Tôhoku Math. J., 8 (1956), 13–28), (Tôhoku Math. J., 11 (1959), 327–350) and Ia. L. Sapiro (Izv. Bysh. Uceb. Zaved. Mat. no6, (1972), 78–85, Russian), (Izv. Bysh. Uceb. Zaved. Mat. no4, (1974), 104–113, Russian) is given. Thus a characterization of a class of topological spaces covered by a product space is obtained and the...
On spaces whose product with every Lindelöf space is Lindelöf
On spaces with the property of weak approximation by points
A sufficient condition that the product of two compact spaces has the property of weak approximation by points (briefly WAP) is given. It follows that the product of the unit interval with a compact WAP space is also a WAP space.
On -starcompact spaces.
On -starcompact spaces
A space is -starcompact if for every open cover of there exists a Lindelöf subset of such that We clarify the relations between -starcompact spaces and other related spaces and investigate topological properties of -starcompact spaces. A question of Hiremath is answered.
On supercomplete uniform spaces IV: Countable products
On supercomplete uniform spaces V: Tamano's product problem
On symmetric products
On the 2-homogeneity of Cartesian products
On the cardinality of power homogeneous Hausdorff spaces
We prove that the cardinality of power homogeneous Hausdorff spaces X is bounded by . This inequality improves many known results and it also solves a question by J. van Mill. We further introduce Δ-power homogeneity, which leads to a new proof of van Douwen’s theorem.
On the class of all spaces of weight not greater than ω_1 whose Cartesian product with every Lindelöf space is Lindelöf
On the Compactness and Countable Compactness of in ZF
In the framework of ZF (Zermelo-Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements " is countably compact" and " is compact"
On the deficiency of product spaces
On the division by Rn.
On the fundamental dimension of the Cartesian product of compacta with the fundamental dimension 2
On the homogeneity of the Tychonoff cube
On the locally fine construction in uniform spaces, locales and formal spaces
On the Nachbin compactification of products of totally ordered spaces.
On the preservation of separation axioms in products
We give sufficient and necessary conditions to be fulfilled by a filter and an ideal in order that the -quotient space of the -ideal product space preserves -properties () (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.