Applied General Topology - Vol 19, No 2 (2018)
https://riunet.upv.es:443/handle/10251/109298
2022-01-28T21:42:55ZOn Reich type λ−α-nonexpansive mapping in Banach spaces with applications to L1([0,1])
https://riunet.upv.es:443/handle/10251/109480
On Reich type λ−α-nonexpansive mapping in Banach spaces with applications to L1([0,1])
Belbaki, Rabah; Karapinar, E.; Ould-Hammouda, Amar
[EN] In this manuscript we introduce a new class of monotone generalized nonexpansive mappings and establish some weak and strong convergence theorems for Krasnoselskii iteration in the setting of a Banach space with partial order. We consider also an application to the space L1([0,1]). Our results generalize and unify the several related results in the literature.
2018-10-05T08:01:06ZA note about various types of sensitivity in general semiflows
https://riunet.upv.es:443/handle/10251/109476
A note about various types of sensitivity in general semiflows
Miller, Alica
[EN] We discuss the implications between various types of sensitivity in general semiflows (sensitivity, syndetic sensitivity, thick sensitivity, thick syndetic sensitivity, multisensitivity, periodic sensitivity, thick periodic sensitivity), including the weak mixing as a very strong type of sensitivity and the strong mixing as the strongest of all type of sensitivity.
2018-10-05T07:56:05ZMore on the cardinality of a topological space
https://riunet.upv.es:443/handle/10251/109471
More on the cardinality of a topological space
Bonanzinga, M.; Carlson, N.; Cuzzupè, M. V.; Stavrova, D.
[EN] In this paper we continue to investigate the impact that various separation axioms and covering properties have onto the cardinality of topological spaces. Many authors have been working in that field. To mention a few, let us refer to results by Arhangel’skii, Alas, Hajnal-Juhász, Bell-Gisburg-Woods, Dissanayake-Willard, Schröder and to the excellent survey by Hodel “Arhangel’skii’s Solution to Alexandroff’s problem: A survey”.Here we provide improvements and analogues of some of the results obtained by the above authors in the settings of more general separation axioms and cardinal invariants related to them. We also provide partial answer to Arhangel’skii’s question concerning whether the continuum is an upper bound for the cardinality of a Hausdorff Lindelöf space having countable pseudo-character (i.e., points are Gδ). Shelah in 1978 was the first to give a consistent negative answer to Arhangel’skii’s question; in 1993 Gorelic established an improved result; and further results were obtained by Tall in 1995. The question of whether or not there is a consistent bound on the cardinality of Hausdorff Lindelöf spaces with countable pseudo-character is still open. In this paper we introduce the Hausdorff point separating weight Hpw(X), and prove that (1) |X| ≤ Hpsw(X)aLc(X)ψ(X), for Hausdorff spaces and (2) |X| ≤ Hpsw(X)ωLc(X)ψ(X), where X is a Hausdorff space with a π-base consisting of compact sets with non-empty interior. In 1993 Schröder proved an analogue of Hajnal and Juhasz inequality |X| ≤ 2c(X)χ(X) for Hausdorff spaces, for Urysohn spaces by considering weaker invariant - Urysohn cellularity Uc(X) instead of cellularity c(X). We introduce the n-Urysohn cellularity n-Uc(X) (where n≥2) and prove that the previous inequality is true in the class of n-Urysohn spaces replacing Uc(X) by the weaker n-Uc(X). We also show that |X| ≤ 2Uc(X)πχ(X) if X is a power homogeneous Urysohn space.
2018-10-05T07:49:17ZOn the essentiality and primeness of λ-super socle of C(X)
https://riunet.upv.es:443/handle/10251/109462
On the essentiality and primeness of λ-super socle of C(X)
Mehran, S.; Namdari, M.; Soltanpour, S.
[EN] Spaces X for which the annihilator of Sλ(X), the λ-super socle of C(X) (i.e., the set of elements of C(X) that cardinality of their cozerosets are less than λ, where λ is a regular cardinal number such that λ≤|X|) is generated by an idempotent are characterized. This enables us to find a topological property equivalent to essentiality of Sλ(X). It is proved that every prime ideal in C(X) containing Sλ(X) is essential and it is an intersection of free prime ideals. Primeness of Sλ(X) is characterized via a fixed maximal ideal of C(X).
2018-10-05T07:44:27Zτ-metrizable spaces
https://riunet.upv.es:443/handle/10251/109460
τ-metrizable spaces
Megaritis, A.C.
[EN] In [1], A. A. Borubaev introduced the concept of τ-metric space, where τ is an arbitrary cardinal number. The class of τ-metric spaces as τ runs through the cardinal numbers contains all ordinary metric spaces (for τ = 1) and thus these spaces are a generalization of metric spaces. In this paper the notion of τ-metrizable space is considered.
2018-10-05T07:39:25ZThe hull orthogonal of the unit inteval [0,1]
https://riunet.upv.es:443/handle/10251/109459
The hull orthogonal of the unit inteval [0,1]
Lazaar, Sami; Nacib, Saber
[EN] In this paper, the full subcategory Hcomp of Top whose objects are Hausdorff compact spaces is identified as the orthogonal hull of the unit interval I = [0,1]. The family of continuous maps rendered invertible by the reflector β◦ρ is deduced.
2018-10-05T07:35:44ZDynamics of real projective transformations
https://riunet.upv.es:443/handle/10251/109456
Dynamics of real projective transformations
Gopal, Sharan; Ravulapalli, Srikanth
[EN] The dynamics of a projective transformation on a real projective space are studied in this paper. The two main aspects of these transformations that are studied here are the topological entropy and the zeta function. Topological entropy is an inherent property of a dynamical system whereas the zeta function is a useful tool for the study of periodic points. We find the zeta function for a general projective transformation but entropy only for certain transformations on the real projective line.
2018-10-05T07:30:23ZCompletely simple endomorphism rings of modules
https://riunet.upv.es:443/handle/10251/109451
Completely simple endomorphism rings of modules
Bovdi, Victor; Salim, Mohamed; Ursul, Mihail
[EN] It is proved that if Ap is a countable elementary abelian p-group, then: (i) The ring End (Ap) does not admit a nondiscrete locally compact ring topology. (ii) Under (CH) the simple ring End (Ap)/I, where I is the ideal of End (Ap) consisting of all endomorphisms with finite images, does not admit a nondiscrete locally compact ring topology. (iii) The finite topology on End (Ap) is the only second metrizable ring topology on it. Moreover, a characterization of completely simple endomorphism rings of modules over commutative rings is obtained.
2018-10-05T07:24:29ZTopological characterization of Gelfand and zero dimensional semirings
https://riunet.upv.es:443/handle/10251/109448
Topological characterization of Gelfand and zero dimensional semirings
Vielma, Jorge; Marchan, Luz
[EN] Let R be a conmutative semiring with 0 and 1, and let Spec(R) be the set of all proper prime ideals of R. Spec(R) can be endowed with two topologies, the Zariski topology and the D-topology. Let Max R denote the set of all maximals prime ideals of R. We prove that the two topologies coincide on Spec(R) and on Max R if and only if R is zero dimensional and Gelfand semiring, respectively.
2018-10-05T07:18:12ZOn rings of real valued clopen continuous functions
https://riunet.upv.es:443/handle/10251/109446
On rings of real valued clopen continuous functions
Afrooz, Susan; Azarpanah, Fariborz; Etebar, Masoomeh
[EN] Among variant kinds of strong continuity in the literature, the clopen continuity or cl-supercontinuity (i.e., inverse image of every open set is a union of clopen sets) is considered in this paper. We investigate and study the ring Cs(X) of all real valued clopen continuous functions on a topological space X. It is shown that every ƒ ∈ Cs(X) is constant on each quasi-component in X and using this fact we show that Cs(X) ≅ C(Y), where Y is a zero-dimensional s-quotient space of X. Whenever X is locally connected, we observe that Cs(X) ≅ C(Y), where Y is a discrete space. Maximal ideals of Cs(X) are characterized in terms of quasi-components in X and it turns out that X is mildly compact(every clopen cover has a finite subcover) if and only if every maximal ideal of Cs(X)is fixed. It is shown that the socle of Cs(X) is an essential ideal if and only if the union of all open quasi-components in X is s-dense. Finally the counterparts of some familiar spaces, such as Ps-spaces, almost Ps-spaces, s-basically and s-extremally disconnected spaces are defined and some algebraic characterizations of them are given via the ring Cs(X).
2018-10-05T07:11:57Z