Projectively generated convergence of sequences
Properties of complements in the lattice of convergence structures.
Pseudouniform topologies on given by ideals
Given a Tychonoff space , a base for an ideal on is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.
Quasi -compact spaces
Quasinormal convergence
Quelques aspects de la dualité en analyse fonctionnelle
Raster convergence with respect to a closure operator
Rationals as a non-trivial complete convergence group
Rationals with exotic convergences
Reflecting Lindelöf and converging ω₁-sequences
We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging ω-sequence or a non-trivial converging ω₁-sequence. We establish that this dichotomy holds in a variety of models; these include the Cohen models, the random real models and any model obtained from a model of CH by an iteration of property K posets. In fact in these models every compact Hausdorff space without non-trivial converging ω₁-sequences is first-countable and, in addition,...
Regular Convergence Spaces.
Regular -spaces
Regularity and extension of mappings in sequential spaces
Regularity and extension of maps
Regularity in convergence spaces
Regular-uniform convergence and the open-open topology.
Relative injectivity as cocompleteness for a class of distributors.
Relatively coarse sequential convergence
We generalize the notion of a coarse sequential convergence compatible with an algebraic structure to a coarse one in a given class of convergences. In particular, we investigate coarseness in the class of all compatible convergences (with unique limits) the restriction of which to a given subset is fixed. We characterize such convergences and study relative coarseness in connection with extensions and completions of groups and rings. E.g., we show that: (i) each relatively coarse dense group precompletion...
Relatively maximal convergences
Topologie, pretopologie, paratopologie e pseudotopologie sono importanti classi di convergenze, chiuse per estremi superiori (superiormente chiuse) ed inoltre caratterizzabili mediante le aderenze di certi filtri. Convergenze -massimali in una classe superiormente chiusa , cioè massimali fra le -convergenze aventi la stessa imagine per la proiezione su , svolgono un ruolo importante nella teoria dei quozienti; infatti, una mappa -quoziente sulla convergenza -massimale in è automaticamente...
Remarks on cardinal inequalities in convergence spaces
We extend the Noble and Ulmer theorem and the Juhász and Hajnal theorems in set-theoretic topology. We show that a statement analogous to that in the former theorem is valid for a family of almost topological convergences, whereas statements analogous to those in the latter theorems hold for a pretopologically Hausdorff convergence.