Regular generalized -closed sets.
Regular -fuzzy topological spaces and their topological modifications.
Regular -spaces
Regular spaces of small extent are ω-resolvable
We improve some results of Pavlov and Filatova, concerning a problem of Malykhin, by showing that every regular space X that satisfies Δ(X) > e(X) is ω-resolvable. Here Δ(X), the dispersion character of X, is the smallest size of a non-empty open set in X, and e(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are ω-resolvable. We also prove that any regular...
Regularity and extension of mappings in sequential spaces
Regularity and extension of maps
Regularity and normality on L-topological spaces. I.
Regularity in convergence spaces
Regular-uniform convergence and the open-open topology.
Related fixed point theorems in fuzzy metric spaces.
Relations and topologies
Relations between some topologies
Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics.
Relative compactness and recent common generalizations of metric and locally compact spaces
Relative injectivity as cocompleteness for a class of distributors.
Relative symmetrizability and metrizability
Relative metrizability is defined and connections with other relative properties are established.
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...
Remainders of metrizable and close to metrizable spaces
We continue the study of remainders of metrizable spaces, expanding and applying results obtained in [Fund. Math. 215 (2011)]. Some new facts are established. In particular, the closure of any countable subset in the remainder of a metrizable space is a Lindelöf p-space. Hence, if a remainder of a metrizable space is separable, then this remainder is a Lindelöf p-space. If the density of a remainder Y of a metrizable space does not exceed , then Y is a Lindelöf Σ-space. We also show that many of...
Remarks about Toronto spaces.