A generalization of -compact spaces
A generalization of Magill's Theorem for non-locally compact spaces
In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature of the...
A hereditarily normal strongly zero-dimensional space with a subspace of positive dimension and an N-compact space of positive dimension
A little more on the product of two pseudocompact spaces
A metrization theorem for countably compact spaces
A new characterization of Eberlein compacta
We give a sufficient and necessary condition for a Radon-Nikodým compact space to be Eberlein compact in terms of a separable fibre connecting weak-* and norm approximation.
A new extension of countable compactness
A new kind of compactness for topological spaces
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 note on characterizations of compactness.
A note on dense subspaces of dyadic compact spaces
A note on E-compact spaces
A note on pairwise c-compact bitopological spaces
A note on strong compactness and S-closedness
A note on zero-dimensional preimages of compact spaces
A Property Between Compact and Strongly Countably Compact
A Ramsey theorem for polyadic spaces
A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin and M. Wage....
A theorem on the weak topology of C(X) for compact scattered X
A Topological Notion of Boundedness.
A unified theory of weak separation properties.