On unified theory for continuities.
On weaker forms of compactness, Lindelöfness, and countable compactness.
On --open sets and a decomposition of almost--continuity.
On -closed sets and some forms of continuity
In this paper, we further the study of -compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using -open and -open sets. Among other results, it is shown a weakly -retract of a Hausdorff space is a -closed subset of .
On -continuity and strong -continuity.
On -regular spaces.
Onto Gelfand maps : appendix
Opérations de Hausdorff itérées et réunions croissantes de compacts
In this paper, motivated by questions in Harmonic Analysis, we study the operation of (countable) increasing union, and show it is not idempotent: iterations are needed in general to obtain the closure of a class under this operation. Increasing union is a particular Hausdorff operation, and we present the combinatorial tools which allow to study the power of various Hausdorff operations, and of their iterates. Besides countable increasing union, we study in detail a related Hausdorff operation,...
Operator compactification of topological spaces.
Order intervals in . Compactness, coincidence of topologies, metrizability
Let be a compact space and let be the Banach lattice of real-valued continuous functions on . We establish eleven conditions equivalent to the strong compactness of the order interval in , including the following ones: (i) consists of isolated points of ; (ii) is pointwise compact; (iii) is weakly compact; (iv) the strong topology and that of pointwise convergence coincide on ; (v) the strong and weak topologies coincide on . Moreover, the weak topology and that of pointwise convergence...
Order-like structure of monotonically normal spaces
For a compact monotonically normal space X we prove: (1) has a dense set of points with a well-ordered neighborhood base (and so is co-absolute with a compact orderable space); (2) each point of has a well-ordered neighborhood -base (answering a question of Arhangel’skii); (3) is hereditarily paracompact iff has countable tightness. In the process we introduce weak-tightness, a notion key to the results above and yielding some cardinal function results on monotonically normal...