On the fundamental dimension of approximatively 1-connected compacta
On the level spaces of fuzzy topological spaces.
On the Noetherian type of topological spaces
The Noetherian type of topological spaces is introduced. Connections between the Noetherian type and other cardinal functions of topological spaces are obtained.
On the problem of preserving the class of continuous real functions
On the product of a compact space with an hereditarily absolutely countably compact space
We show that the product of a compact, sequential space with an hereditarily absolutely countably compact space is hereditarily absolutely countably compact, and further that the product of a compact space of countable tightness with an hereditarily absolutely countably compact -bounded space is hereditarily absolutely countably compact.
On the separation properties of
On the set-theoretic strength of the n-compactness of generalized Cantor cubes
We investigate, in set theory without the Axiom of Choice , the set-theoretic strength of the statement Q(n): For every infinite set X, the Tychonoff product , where 2 = 0,1 has the discrete topology, is n-compact, where n = 2,3,4,5 (definitions are given in Section 1). We establish the following results: (1) For n = 3,4,5, Q(n) is, in (Zermelo-Fraenkel set theory minus ), equivalent to the Boolean Prime Ideal Theorem , whereas (2) Q(2) is strictly weaker than in set theory (Zermelo-Fraenkel set...
On the ΄΄Fragmentation΄΄ of Certain Pseydocompact Groups
On thick spaces
On topologies of free groups
On typical parametrizations of finite-dimensional compacta on the Cantor set
We prove that if X is a perfect finite-dimensional compactum, then for almost every continuous surjection of the Cantor set onto X, the set of points of maximal order is uncountable. Moreover, if X is a perfect compactum of positive finite dimension then for a typical parametrization of X on the Cantor set, the set of points of maximal order is homeomorphic to the product of the rationals and the Cantor set.
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.