Applied General Topology - Vol 16, No 2 (2015)
https://riunet.upv.es:443/handle/10251/72413
2019-12-07T22:31:36ZTwo general fixed point theorems for a sequence of mappings satisfying implicit relations in Gp - metric spaces
https://riunet.upv.es:443/handle/10251/72545
Two general fixed point theorems for a sequence of mappings satisfying implicit relations in Gp - metric spaces
Popa, Valeriu; Patriciu, Alina-Mihaela
[EN] In this paper, two general fixed point theorem for a sequence of mappings satisfying implicit relations in Gp - complete metric spaces are proved.
2016-10-21T07:09:42ZThe dynamical look at the subsets of a group
https://riunet.upv.es:443/handle/10251/72544
The dynamical look at the subsets of a group
Protasov, Igor V.; Slobodianiuk, Serhii
[EN] We consider the action of a group $G$ on the family $\mathcal{P}(G)$ of all subsets of $G$ by the right shifts $A\mapsto Ag$ and give the dynamical characterizations of thin, $n$-thin, sparse and scattered subsets.For $n\in\mathbb{N}$, a subset $A$ of a group $G$ is called $n$-thin if $g_0A\cap\dots\cap g_nA$ is finite for all distinct $g_0,\dots,g_n\in G$.Each $n$-thin subset of a group of cardinality $\aleph_0$ can be partitioned into $n$ $1$-thin subsets but there is a $2$-thin subset in some Abelian group of cardinality $\aleph_2$ which cannot be partitioned into two $1$-thin subsets. We eliminate the gap between $\aleph_0$ and $\aleph_2$ proving that each $n$-thin subset of an Abelian group of cardinality $\aleph_1$ can be partitioned into $n$ $1$-thin subsets.
2016-10-21T07:07:35ZSome classes of minimally almost periodic topological groups
https://riunet.upv.es:443/handle/10251/72542
Some classes of minimally almost periodic topological groups
Comfort, Wistar; Gould, Franklin R.
[EN] A Hausdorff topological group G=(G,T) has the small subgroup generating property (briefly: has the SSGP property, or is an SSGP group) if for each neighborhood U of $1_G$ there is a family $\sH$ of subgroups of $G$ such that $\bigcup\sH\subseteq U$ and $\langle\bigcup\sH\rangle$ is dense in $G$. The class of \rm{SSGP}$ groups is defined and investigated with respect to the properties usually studied by topologists (products, quotients, passage to dense subgroups, and the like), and with respect to the familiar class of minimally almost periodic groups (the m.a.p. groups). Additional classes SSGP(n) for $n<\omega$ (with SSGP(1) = SSGP) are defined and investigated, and the class-theoretic inclusions $$\mathrm{SSGP}(n)\subseteq\mathrm{SSGP}(n+1)\subseteq\mathrm{ m.a.p.}$$ are established and shown proper.In passing the authors also establish the presence of {\rm SSGP}$(1)$ or {\rm SSGP}$(2)$ in many of the early examples in the literature of abelian m.a.p. groups.
This paper derives from and extends selected portions of theDoctoral Dissertation [19],written at Wesleyan University (Middletown, Connecticut,USA) by the second-listed co-author under the guidance of the first-listed co-author.
2016-10-21T07:04:59ZRational criterion testing the density of additive subgroups of R^n and C^n
https://riunet.upv.es:443/handle/10251/72540
Rational criterion testing the density of additive subgroups of R^n and C^n
Elghaoui, Mohamed; Ayadi, Adlene
[EN] In this paper, we give an explicit criterion to decide thedensity of finitely generated additive subgroups of R^n and C^n.
2016-10-21T07:02:01ZPrimal spaces and quasihomeomorphisms
https://riunet.upv.es:443/handle/10251/72539
Primal spaces and quasihomeomorphisms
Haouati, Afef; Lazaar, Sami
[EN] In [3], the author has introduced the notion of primal spaces.The present paper is devoted to shedding some light on relations between quasihomeomorphisms and primal spaces.Given a quasihomeomorphism q from X to Y , where X and Y are principal spaces, we are concerned specically with a main problem: what additional conditions have to be imposed on q in order to render X (resp.Y ) primal when Y (resp.X) is primal.
2016-10-21T06:59:07ZOn the locally functionally countable subalgebra of C(X) on locally functionally countable subalgebra of C(X)
https://riunet.upv.es:443/handle/10251/72428
On the locally functionally countable subalgebra of C(X) on locally functionally countable subalgebra of C(X)
Karamzadeh, O. A. S.; Namdari, M.; Soltanpour, S.
[EN] Let $C_c(X)=\{f\in C(X) : |f(X)|\leq \aleph_0\}$, $C^F(X)=\{f\in C(X): |f(X)|<\infty\}$, and $L_c(X)=\{f\in C(X) : \overline{C_f}=X\}$, where $C_f$ is the union of all open subsets $U\subseteq X$ such that $|f(U)|\leq\aleph_0$, and $C_F(X)$ be the socle of $C(X)$ (i.e., the sum of minimal ideals of $C(X)$). It is shown that if $X$ is a locally compact space, then $L_c(X)=C(X)$ if and only if $X$ is locally scattered.We observe that $L_c(X)$ enjoys most of the important properties which are shared by $C(X)$ and $C_c(X)$. Spaces $X$ such that $L_c(X)$ is regular (von Neumann) are characterized. Similarly to $C(X)$ and $C_c(X)$, it is shown that $L_c(X)$ is a regular ring if and only if it is $\aleph_0$-selfinjective.We also determine spaces $X$ such that ${\rm Soc}{\big(}L_c(X){\big)}=C_F(X)$ (resp., ${\rm Soc}{\big(}L_c(X){\big)}={\rm Soc}{\big(}C_c(X){\big)}$). It is proved that if $C_F(X)$ is a maximal ideal in $L_c(X)$, then $C_c(X)=C^F(X)=L_c(X)\cong \prod\limits_{i=1}^n R_i$, where $R_i=\mathbb R$ for each $i$, and $X$ has a unique infinite clopen connected subset. The converse of the latter result is also given. The spaces $X$ for which $C_F(X)$ is a prime ideal in $L_c(X)$ are characterized and consequently for these spaces, we infer that $L_c(X)$ can not be isomorphic to any $C(Y)$.
2016-10-20T13:31:47ZOn cyclic relatively nonexpansive mappings in generalized semimetric spaces
https://riunet.upv.es:443/handle/10251/72427
On cyclic relatively nonexpansive mappings in generalized semimetric spaces
Gabeleh, Moosa
[EN] In this article, we prove a fixed point theorem for cyclic relatively nonexpansive mappings in the setting of generalized semimetric spaces by using a geometric notion of seminormal structure and then we conclude some results in uniformly convex Banach spaces. We also discuss on the stability of seminormal structure in generalized semimetric spaces.
2016-10-20T13:29:25ZLebesgue quasi-uniformity on textures
https://riunet.upv.es:443/handle/10251/72426
Lebesgue quasi-uniformity on textures
Ozcag, Selma
[EN] This is a continuation of the work where the notions of Lebesgue uniformity and Lebesgue quasi uniformity in a texture space were introduced. It is well known that the quasi uniform space with a compact topology has the Lebesgue property. This result is extended to direlational quasi uniformities and dual dicovering quasi uniformities. Additionally we discuss the completeness of lebesgue di-uniformities and dual dicovering lebesgue di-uniformities.
2016-10-20T13:27:18ZFree paratopological groups
https://riunet.upv.es:443/handle/10251/72425
Free paratopological groups
Elfard, Ali Sayed
[EN] Let FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X) on a $P_\alpha$-space $X$ where $\alpha$ is an infinite cardinal and then we prove that the group FP(X) is an Alexandroff space if X is an Alexandroff space. Moreover, we introduce a~neighborhood base at the identity of the group FP(X) when the space X is Alexandroff and then we give some properties of this neighborhood base. As applications of these, we prove that the group FP(X) is T_0 if X is T_0, we characterize the spaces X for which the group FP(X) is a topological group and then we give a class of spaces $X$ for which the group FP(X) has the inductive limit property.
2016-10-20T13:23:47ZFinite products of limits of direct systems induced by maps
https://riunet.upv.es:443/handle/10251/72424
Finite products of limits of direct systems induced by maps
Ivansic, Ivan; Rubin, Leonard R.
[EN] Let Z, H be spaces. In previous work, we introduced the direct (inclusion) system induced by the set of maps between the spaces Z and H. Its direct limit is a subset of Z × H, but its topology is different from the relative topology. We found that many of the spaces constructed from this method are pseudo-compact and Tychonoff. We are going to show herein that these spaces are typically not sequentially compact and we will explore conditions under which a finite product of them will be pseudo-compact.
2016-10-20T13:17:20Z