Applied General Topology - Vol 14, No 1 (2013)
https://riunet.upv.es:443/handle/10251/87455
2024-04-23T17:04:51ZPseudo perfectly continuous functions and closedness/compactness of their function spaces
https://riunet.upv.es:443/handle/10251/87472
Pseudo perfectly continuous functions and closedness/compactness of their function spaces
Kohli, J.K.; Singh, D.; Aggarwal, Jeetendra; Rana, Manoj
[EN] A new class of functions called 'pseudo perfectly continuous' functions is introduced. Their place in the hierarchy of variants of continuity which already exist in the literature is highlighted. The interplay between topological properties and pseudo perfect continuity is investigated. Function spaces of pseudo perfectly continuous functions are considered and sufficient conditions for their closedness and compactness in the topology of pointwise convergence are formulated.
2017-09-19T07:15:30ZF-door spaces and F-submaximal spaces
https://riunet.upv.es:443/handle/10251/87470
F-door spaces and F-submaximal spaces
Dridi, Lobna; Lazaar, Sami; Turki, Tarek
[EN] Submaximal spaces and door spaces play an enigmatic role in topology. In this paper, reinforcing this role, we are concerned with reaching two main goals:
The first one is to characterize topological spaces X such that F(X) is a submaximal space (resp., door space) for some covariant functor Ff rom the category Top to itself. T0, and FH functors are completely studied.
Secondly, our interest is directed towards the characterization of maps f given by a flow (X, f) in the category Set, such that (X,P(f)) is submaximal (resp., door) where P(f) is a topology on X whose closed sets are exactly the f-invariant sets.
2017-09-19T07:13:39ZStrongly path-confluent mappings
https://riunet.upv.es:443/handle/10251/87469
Strongly path-confluent mappings
Qahis, Abdo; Noorani, Mohd. Salmi Md.
[EN] In this paper, we introduce a new class of path-confluent mapping, called strongly path-confluent maps. We discuss and study some characterizations and some basic properties of this class of mappings. Relations between this class and some other existing classes of mappings are also obtained. Also we study some operations on this class of mappings, such as: composition property, composition factor property, component restriction property and path-component restriction property.
2017-09-19T07:11:15ZThe hyperspaces Cn(X) for finite ray-graphs
https://riunet.upv.es:443/handle/10251/87467
The hyperspaces Cn(X) for finite ray-graphs
Esty, Norah
[EN] In this paper we consider the hyperspace Cn(X) of non-empty and closed subsets of a base space X with up to n connected components. The class of base spaces we consider we call finite ray-graphs, and are a noncompact variation on finite graphs. We prove two results about the structure of these hyperspaces under different topologies (Hausdorff metric topology and Vietoris topology).
2017-09-19T07:07:37ZA notion of continuity in discrete spaces and applications
https://riunet.upv.es:443/handle/10251/87466
A notion of continuity in discrete spaces and applications
Capraro, Valerio
[EN] We propose a notion of continuous path for locally finite metric spaces, taking inspiration from the recent development of A-theory for locally finite connected graphs. We use this notion of continuity to derive an analogue in Z2 of the Jordan curve theorem and to extend to a quite large class of locally finite metric spaces (containing all finite metric spaces) an inequality for the ℓp-distortion of a metric space that has been recently proved by Pierre-Nicolas Jolissaint and Alain Valette for finite connected graphs.
2017-09-19T07:05:59ZA RAFU linear space uniformly dense in C [a, b]
https://riunet.upv.es:443/handle/10251/87464
A RAFU linear space uniformly dense in C [a, b]
Corbacho Cortés, E.
[EN] In this paper we prove that a RAFU (radical functions) linear space, ∁, is uniformly dense in C [a, b] by means of a S-separation condition of certain subsets of [a, b] due to Blasco-Moltó. This linear space is not a lattice or an algebra. Given an arbitrary function f 2 C [a, b] we will obtain easily the sequence (Cn)n of ∁ that converges uniformly to f and we will show the degree of uniform approximation to f with (Cn)n.
2017-09-19T07:03:18ZEpimorphisms and maximal covers in categories of compact spaces
https://riunet.upv.es:443/handle/10251/87463
Epimorphisms and maximal covers in categories of compact spaces
Banaschewski, B.; Hager, A.W.
[EN] The category C is "projective complete"if each object has a projective cover (which is then a maximal cover). This property inherits from C to an epireflective full subcategory R provided the epimorphisms in R are also epi in C. When this condition fails, there still may be some maximal covers in R. The main point of this paper is illustration of this in compact Hausdorff spaces with a class of examples, each providing quite strange epimorphisms and maximal covers. These examples are then dualized to a category of algebras providing likewise strange monics and maximal essential extensions.
2017-09-19T07:00:50ZRange-preserving AE(0)-spaces
https://riunet.upv.es:443/handle/10251/87460
Range-preserving AE(0)-spaces
Comfort, W.W.; Hager, A.W.
[EN] All spaces here are Tychonoff spaces. The class AE(0) consists of those spaces which are absolute extensors for compact zero-dimensional spaces. We define and study here the subclass AE(0)rp, consisting of those spaces for which extensions of continuous functions can be chosen to have the same range. We prove these results. If each point of T 2 AE(0) is a G-point of T , then T 2 AE(0)rp. These are equivalent: (a) T 2 AE(0)rp; (b) every compact subspace of T is metrizable; (c) every compact subspace of T is dyadic; and (d) every subspace of T is AE(0). Thus in particular, every metrizable space is an AE(0)rp-space.
2017-09-19T06:58:06ZOn star compactifications
https://riunet.upv.es:443/handle/10251/87459
On star compactifications
Acosta, Lorenzo; Rubio, I. Marcela
[EN] We study the ordered structure of the collection of star compactifications by n points and the behavior of these compactifications through quotients obtained by identification of additional points.
2017-09-19T06:55:44ZUpper and lower cl-supercontinuous multifunctions
https://riunet.upv.es:443/handle/10251/87456
Upper and lower cl-supercontinuous multifunctions
Kohli, J.K.; Arya, Chaman Prakash
[EN] The notion of cl-supercontinuity ( clopen continuity) of functions is extended to the realm of multifunctions. Basic properties of upper(lower) cl-supercontinuous multifunctions are studied and their place in the hierarchy of strong variants of continuity of multifunctions is discussed. Examples are included to reflect upon the distinctiveness of upper (lower) cl-supercontinuity of multifunctions from that of othe rstrong variants of continuity of multifunctions which already exist in the literature.
2017-09-19T06:48:01Z