Sur quelques points de topologie générale. Théorie des nasses et des tramails
Sur trois questions de Grimeisen en topologie générale
Sur un théorème de métrisabilité.
S-Weakly Hausdorff Spaces
and objects at in the category of proximity spaces
In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various , , , structures at a point are investigated. Finally, we examine the relationships between the generalized separation...
-frames and almost compact frames
-separation axioms on frames
-catégories (catégories dans un triple)
- pairwise continuous functions and bitopological separation axioms
-spaces and the Wallman compactification.
Tanaka spaces and products of sequential spaces
We consider properties of Tanaka spaces (introduced in Mynard F., More on strongly sequential spaces, Comment. Math. Univ. Carolin. 43 (2002), 525–530), strongly sequential spaces, and weakly sequential spaces. Applications include product theorems for these types of spaces.
Teilfolgen gleichverteilter Folgen.
Tensor products with bounded continuous functions.
The arbitrary intersection of a family of open subsets with the -s-locally finite property is -semi-open.
The Arkhangel’skiĭ–Tall problem: a consistent counterexample
We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel’skiĭ and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in , and a version of an (ω,1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a poset due to Judah and Shelah for obtaining a Q-set by a countable support iteration.
The Arkhangel'skiĭ–Tall problem under Martin’s Axiom
We show that MA implies that normal locally compact metacompact spaces are paracompact, and that MA() implies normal locally compact metalindelöf spaces are paracompact. The latter result answers a question of S. Watson. The first result implies that there is a model of set theory in which all normal locally compact metacompact spaces are paracompact, yet there is a normal locally compact metalindelöf space which is not paracompact.
The Baire property in remainders of topological groups and other results
It is established that a remainder of a non-locally compact topological group has the Baire property if and only if the space is not Čech-complete. We also show that if is a non-locally compact topological group of countable tightness, then either is submetrizable, or is the Čech-Stone remainder of an arbitrary remainder of . It follows that if and are non-submetrizable topological groups of countable tightness such that some remainders of and are homeomorphic, then the spaces...
The Baire Set Fixing Property and Uniform Continuity in Topological Groups.
The Banach algebra of continuous bounded functions with separable support
We prove a commutative Gelfand-Naimark type theorem, by showing that the set of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space X (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to C₀(Y) for some unique (up to homeomorphism) locally compact Hausdorff space Y. The space Y, which we explicitly construct as a subspace of the Stone-Čech compactification of X, is countably compact, and if X is non-separable,...
The Bohr compactification, modulo a metrizable subgroup
The authors prove the following result, which generalizes a well-known theorem of I. Glicksberg [G]: If G is a locally compact Abelian group with Bohr compactification bG, and if N is a closed metrizable subgroup of bG, then every A ⊆ G satisfies: A·(N ∩ G) is compact in G if and only if {aN:a ∈ A} is compact in bG/N. Examples are given to show: (a) the asserted equivalence can fail in the absence of the metrizability hypothesis, even when N ∩ G = {1}; (b) the asserted equivalence can hold for suitable...