Rare -continuity.
Raster convergence with respect to a closure operator
Realization of Cartesian Closed Topological Hulls.
Realization of mappings
Realizations of topologies and closure operators by set systems and by neighbourhoods
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.