
Popa, Valeriu; Patriciu, AlinaMihaela
[EN] In this paper, two general fixed point theorem for a sequence of mappings satisfying implicit relations in Gp  complete metric spaces are proved.

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...

Comfort, Wistar; Gould, Franklin R.
This paper derives from and extends selected portions of theDoctoral Dissertation [19],written at Wesleyan University (Middletown, Connecticut,USA) by the secondlisted coauthor under the guidance of the firstlisted coauthor.

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.

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.

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...

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.

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 diuniformities and dual dicovering lebesgue diuniformities.

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...

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 pseudocompact 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 pseudocompact.

Felicit, J. Maria; Eldred, A. Anthony
[EN] We consider pcyclic mappings and prove an analogous result to Edelstien contractive theorem for best proximity points. Also we give similar results satisfying BoydWong and Geraghty contractive conditions.