Topological quasitopos hulls of categories containing topological and metric objects
Topological representations of quasiordered sets.
Topologically-algebraic structure functors full reflective or coreflective restrictions of semitopological functors
Topologie su spazi di funzioni derivanti da topologie su iperspazi
Topologie sur l'ensemble des compacts non vides d'un espace topologique séparé. Exemple de complémentaire analytique non analytique dans un espace polonais
Topologies in product which preserve Baire spaces
Topologies on products and decompositions of topological spaces
Topologizing the hypersets.
Topology in a category: Compactness.
Toroidal decompositions of and a family of 3-dimensional ANR’s (AR’s)
Tower extension of topological constructs
Let be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct , called the tower extension of (indexed by ). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spaces and pseudotopological approach spaces, etc, as special cases. It is proved that this process has a lot...
Trivial bundles and near-homeomorphisms
Two non-homeomorphic countable spaces having homeomorphic squares
Two-fold theorem on Fréchetness of products
A refined common generalization of known theorems (Arhangel’skii, Michael, Popov and Rančin) on the Fréchetness of products is proved. A new characterization, in terms of products, of strongly Fréchet topologies is provided.
Tychonoff products of super second countable and super separable metric spaces
Tychonoff Products of Two-Element Sets and Some Weakenings of the Boolean Prime Ideal Theorem
Let X be an infinite set, and (X) the Boolean algebra of subsets of X. We consider the following statements: BPI(X): Every proper filter of (X) can be extended to an ultrafilter. UF(X): (X) has a free ultrafilter. We will show in ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) that the following four statements are equivalent: (i) BPI(ω). (ii) The Tychonoff product , where 2 is the discrete space 0,1, is compact. (iii) The Tychonoff product is compact. (iv) In a Boolean algebra...
Typical sets and typical continuous functions
Ultrafiltres sur un espace spectral - Anneaux de Baer - Anneaux a spectre minimal compact.
Ultraparacompactness in certain Pixley-Roy hyperspaces
Uncountably many wild knots whose cyclic branched covering are S3.
There is a disk in S3 whose interior is PL embedded and whose boundary has a tame Cantor set of locally wild points, such that the n-fold cyclic coverings of S3 branched over the boundary of the disk are all S3. An uncountable set of inequivalent wild knots with these properties is exhibited.