Recent research in hyperspace theory.
Recognition of certain classes of closed maps
Recognizing approximate -tameness.
Recognizing the topology of the space of closed convex subsets of a Banach space
Rectangular covers of products missing diagonals
We give a characterization of a paracompact -space to have a -diagonal in terms of three rectangular covers of . Moreover, we show that a local property and a global property of a space are given by the orthocompactness of .
Reducing inverse systems of monomorphisms
Regular closure operators and compactness
Regular maps and products of p-quotient maps
Regular -spaces
Regularity and extension of mappings in sequential spaces
Relations approximated by continuous functions in the Vietoris topology
Let X be a Tikhonov space, C(X) be the space of all continuous real-valued functions defined on X, and CL(X×ℝ) be the hyperspace of all nonempty closed subsets of X×ℝ. We prove the following result: Let X be a locally connected locally compact paracompact space, and let F ∈ CL(X×ℝ). Then F is in the closure of C(X) in CL(X×ℝ) with the Vietoris topology if and only if: (1) for every x ∈ X, F(x) is nonempty; (2) for every x ∈ X, F(x) is connected; (3) for every isolated x ∈ X, F(x) is a singleton...
Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics.
Relative Compactness for Hyperspaces
The present paper contains results characterizing relatively compact subsets of the space of the closed subsets of a metrizable space, equipped with various hypertopologies. We investigate the hyperspace topologies that admit a representation as weak topologies generated by families of gap functionals defined on closed sets, as well as hit-and-miss topologies and proximal-hit and-miss topologies.
Relative continuity of the functor
Relative injectivity as cocompleteness for a class of distributors.
Relative normality and product spaces
Arhangel’skiĭ defines in [Topology Appl. 70 (1996), 87–99], as one of various notions on relative topological properties, strong normality of in for a subspace of a topological space , and shows that this is equivalent to normality of , where denotes the space obtained from by making each point of isolated. In this paper we investigate for a space , its subspace and a space the normality of the product in connection with the normality of . The cases for paracompactness, more...
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 on Cartesian products
Remarks on cellularity in products