A factorization lemma and its application to realization of mappings as inverse limits
A few Remarks on Reduced Ideal-products
A few topological problems
A functional representation of the hyperspace monad
A functional representation of the hyperspace monad, based on the semilattice structure of function space, is constructed.
A fuzzy modification of the category of linearly ordered spaces
A generalization of boundedly compact metric spaces
A metric space is called a space provided each continuous function on into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that spaces play relative to the compact metric spaces.
A generalization of Čech-complete spaces and Lindelöf -spaces
The class of -spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf -spaces, metrizable spaces with the weight , but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that -spaces are in a duality with Lindelöf -spaces: is an -space if and only if some (every) remainder of in a compactification is a Lindelöf -space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math. 220 (2013),...
A generalized continuity and product spaces
A hit-and-miss topology for , Cₙ(X) and Fₙ(X)
A hit-and-miss topology () is defined for the hyperspaces , Cₙ(X) and Fₙ(X) of a continuum X. We study the relationship between and the Vietoris topology and we find conditions on X for which these topologies are equivalent.
A large -discrete Fréchet space having the Souslin property
A Lindelöf space X such that is normal but not paracompact
A maximal chain approach to topology and order.
A new approach to a hyperspace theory.
A new hyperspace topology and the study of the function space -
A nice class extracted from -theory
We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, -stable and -monolithic. It is also established that any Sokolov compact space is Fréchet-Urysohn and the space is Lindelöf. We prove that any Sokolov space with a -diagonal has a countable network and obtain some cardinality restrictions on subsets...
A non-Tychonoff relatively normal subspace
This paper presents a new consistent example of a relatively normal subspace which is not Tychonoff.
A normal space X for which X×I is not normal
A note on collectionwise normality and product spaces
A note on dense subspaces of dyadic compact spaces
A note on exponentiation in regular locales