Relations between ß X / X and a Certain Subspace of ... X.
Relations between the -completeness and the paracompactness of closure spaces
Relations on topological spaces
Relationship among various Vietoris-type and microsimplicial homology theories
In this paper, we clarify the relationship among the Vietoris-type homology theories and the microsimplicial homology theories, where the latter are nonstandard homology theories defined by M.C. McCord (for topological spaces), T. Korppi (for completely regular topological spaces) and the author (for uniform spaces). We show that McCord’s and our homology are isomorphic for all compact uniform spaces and that Korppi’s and our homology are isomorphic for all fine uniform spaces. Our homology shares...
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 compactness and recent common generalizations of metric and locally compact spaces
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 connectednesses and disconnectednesses in topological categories
Relative continuity of the functor
Relative directed homotopy theory of partially ordered spaces.
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...
Relative symmetrizability and metrizability
Relative metrizability is defined and connections with other relative properties are established.
Relatively absolutely countably compact spaces.
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 compact spaces and separation properties
We consider the property of relative compactness of subspaces of Hausdorff spaces. Several examples of relatively compact spaces are given. We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space.
Relatively complete ordered fields without integer parts
We prove a convenient equivalent criterion for monotone completeness of ordered fields of generalized power series with exponents in a totally ordered Abelian group G and coefficients in an ordered field F. This enables us to provide examples of such fields (monotone complete or otherwise) with or without integer parts, i.e. discrete subrings approximating each element within 1. We include a new and more straightforward proof that is always Scott complete. In contrast, the Puiseux series field...
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...
Relatively minimal extensions of topological flows
The concept of relatively minimal (rel. min.) extensions of topological flows is introduced. Several generalizations of properties of minimal extensions are shown. In particular the following extensions are rel. min.: distal point transitive, inverse limits of rel. min., superpositions of rel. min. Any proximal extension of a flow Y with a dense set of almost periodic (a.p.) points contains a unique subflow which is a relatively minimal extension of Y. All proximal and distal factors of a point...