A separated cell A of a topological space X is a family of pairwise disjoint open sets with the property that, for any partition A= A1 ∪ A2 of A, ⋃ A1 and ⋃ A2 are completely separated. The separated cellularity sc(X) of X is the supremum of all cardinals of separated cells. A space X has finite separation if it has no infinite separated cells. With X compact, every separated cell of X has size...

We study the question "Are discrete families of points separated in countably paracompact spaces?" in the class of first countable spaces and the class of separable spaces. Two of the main directions of research in general topology in the last thirty years have been the work of Jones, Bing, Tall, Fleissner, Nyikos and others motivated by the normal Moore space problem (when are discrete familie...

Let ( X , J ) be an almost complex manifold with a (smooth) involution σ : → such that Fix ≠ ∅ . Assume is conjugation, i.e., the differential of anti-commutes The space P m = S × / ∼ where v x − was referred to as generalized Dold manifold. above definition admits obvious generalization much wider class spaces are arbitrary topological spaces. resulting will called space. When and CW complexes...

M.Radulescu proved the following result: Let X be a compact Hausdorff topological space and π : C(X)→ C(X) a supra-additive and supra-multiplicative operator. Then π is linear and multiplicative. We generalize this result to arbitrary topological spaces.

Let CΨ (X) be the ideal of functions with pseudocompact support and let kX be the set of all points in υX having compact neighborhoods. We show that CΨ (X) is pure if and only if βX−kX is a round subset of βX, CΨ (X) is a projective C(X)-module if and only if CΨ (X) is pure and kX is paracompact. We also show that if CΨ (X) is pure, then for each f ∈ CΨ (X) the ideal (f ) is a projective (flat)...

We formulate the notion of uniformization of colorings of ladder systems on subsets of trees. We prove that Suslin trees have this property and also Aronszajn trees in the presence of Martin’s Axiom. As an application we show that if a tree has this property, then every countable discrete family of subsets of the tree can be separated by a family of pairwise disjoint open sets. Such trees are t...

We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that Cp(X) is hereditarily a D-space whenever X is a Lindelöf Σ-space. This answers a question of Matveev, and improves a result of Buzyakova, who proved the same result for X compact. We also prove that if a ...

Let X be the Bennett-Lutzer’s space and Y be the space obtained from X by shrinking the set of all rational numbers to a point. In his book, G.Gao claimed that the space Y is compact. In this paper, we prove that Y is neither countably compact nor Lindelöf, which shows that G.Gao’s claim is not true. Moreover, we prove that Y is strongly paracompact. As an application of this result, we obtain ...