Applied General Topology
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<p style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 6.0pt; margin-left: 0cm; text-align: justify; text-justify: inter-ideograph;"><span>The international journal <strong>Applied General Topology</strong> publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications.</span></p>en-USThe works published in this journal are subject to the following terms:<br /><ol><li>The journal conserves the patrimonial rights (copyright) of the works published, and encourages and allows the reuse of the same under the license specified in point 2.</li><li>The works are published in the online edition of the journal under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0. You can copy, use, distribute, transmit and publicly display, provided acknowledgment of the authorship, the url, and the journal, and not used for commercial purposes.</li><li>The authors agree with the license used by the journal, with the conditions of self-archiving and the open access policy.</li><li>It allows authors to spread electronically (e.g., in institutional repositories or on their own website) the published version of his works, as it encourages its circulation and diffusion earliest and thus a possible increase in its citation and scope between the academic community.</li></ol>agt@mat.upv.es (Applied General Topology)ojsadmin@upvnet.upv.es (Administrador PoliPapers)Mon, 03 Oct 2016 12:14:23 +0200OJS 2.4.7.1http://blogs.law.harvard.edu/tech/rss60On monotonic bijections on subgroups of R
http://polipapers.upv.es/index.php/AGT/article/view/4116
We show that for any continuous monotonic bijection $f$ on a $\sigma$-compact subgroup $G\subset \mathbb R$ there exists a binary operation $+_f$ such that $\langle G, +_f\rangle$ is a topological group topologically isomorphic to $\langle G, +\rangle$ and $f$ is a shift with respect to $+_f$. We then show that monotonicity cannot be replaced by a periodic-point free continuous bijections. We explore a few routes leading to generalizations and counterexamplesRaushan Buzyakova
Copyright (c) 2016 Applied General Topology
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http://polipapers.upv.es/index.php/AGT/article/view/4116Mon, 03 Oct 2016 12:14:18 +0200Induced dynamics on the hyperspaces
http://polipapers.upv.es/index.php/AGT/article/view/4154
<p> </p><p>In this paper, we study the dynamics induced by finite commutative relation on the hyperspaces. We prove that the dynamics induced on the hyperspace by a non-trivial commutative family of continuous self maps cannot be transitive and hence cannot exhibit higher degrees of mixing. We also prove that the dynamics induced on the hyperspace by such a collection cannot have dense set of periodic points. We also give example to show that the induced dynamics in this case may or may not be sensitive.</p>Puneet Sharma
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http://polipapers.upv.es/index.php/AGT/article/view/4154Mon, 03 Oct 2016 12:14:18 +0200A construction of a fuzzy topology from a strong fuzzy metric
http://polipapers.upv.es/index.php/AGT/article/view/4495
<p>After the inception of the concept of a fuzzy metric by I. Kramosil and J. Michalek, and especially after its revision by A. George and G. Veeramani, the attention of many researches was attracted to the topology induced by a fuzzy metric. In most of the works devoted to this subject the resulting topology is an ordinary, that is a crisp one. Recently some researchers showed interest in the fuzzy-type topologies induced by fuzzy metrics. In particular, in the paper (J.J. Mi\~{n}ana, A. \v{S}ostak, {\it Fuzzifying topology induced by a strong fuzzy metric}, Fuzzy Sets and Systems, 6938 DOI information: 10.1016/j.fss.2015.11.005.) a fuzzifying topology ${\mathcal T}:2^X \to [0,1]$ induced by a fuzzy metric $m: X\times X \times [0,\infty)$ was constructed. In this paper we extend this construction to get the fuzzy topology ${\mathcal T}: [0,1]^X \to [0,1]$ and study some properties of this fuzzy topology.54A</p>Svetlana Grecova, Alexander Sostak, Ingrida Uljane
Copyright (c) 2016 Applied General Topology
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http://polipapers.upv.es/index.php/AGT/article/view/4495Mon, 03 Oct 2016 12:14:19 +0200Results about the Alexandroff duplicate space
http://polipapers.upv.es/index.php/AGT/article/view/4521
In this paper, we present some new results about the Alexandroff Duplicate Space. We prove that if a space X has the property P, then its Alexandroff Duplicate space A(X) may not have P, where P is one of the following properties: extremally disconnected, weakly extremally disconnected, quasi-normal, pseudo compact. We prove that if X is $\alpha$-normal, epinormal, or has property $\omega D$, then so is A(X). We prove almost normality is preserved by A(X) under special conditions.Khulod Almontashery, Lutfi Kalantan
Copyright (c) 2016 Applied General Topology
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http://polipapers.upv.es/index.php/AGT/article/view/4521Mon, 03 Oct 2016 12:14:19 +0200A note on uniform entropy for maps having topological specification property
http://polipapers.upv.es/index.php/AGT/article/view/4555
We prove that if a uniformly continuous self-map $f$ of a uniform space has topological specification property then the map $f$ has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having specification property. An example is also provided to justify that the converse is not true.<br /><br />Sejal Shah, Ruchi Das, Tarun Das
Copyright (c) 2016 Applied General Topology
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http://polipapers.upv.es/index.php/AGT/article/view/4555Mon, 03 Oct 2016 12:14:20 +0200Homeomorphisms on compact metric spaces with finite derived length
http://polipapers.upv.es/index.php/AGT/article/view/4593
<p>The sets of periodic points of self homeomorphisms on an ordinal of finite derived length are characterised, thus characterising the same for homeomorphisms on compact metric spaces with finite derived length. A partition of ordinal is introduced to study this problem which is also used to solve two more problems: one about an equivalence relation and the other about a group action, both on an ordinal of finite derived length.</p>V Kannan, Sharan Gopal
Copyright (c) 2016 Applied General Topology
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http://polipapers.upv.es/index.php/AGT/article/view/4593Mon, 03 Oct 2016 12:14:20 +0200Fundamental groups and Euler characteristics of sphere-like digital images
http://polipapers.upv.es/index.php/AGT/article/view/4624
The current paper focuses on fundamental groups and Euler characteristics of various digital models of the 2-dimensional sphere. For all models that we consider, we show that the fundamental groups are trivial, and compute the Euler characteristics (which are not always equal). We consider the connected sum of digital surfaces and investigate how this operation relates to the fundamental group and Euler characteristic. We also consider two related but dierent notions of a digital image having "no holes," and relate this to the triviality of the fundamental group. Many of our results have origins in the paper [15] by S.-E. Han, which contains many errors. We correct these errors when possible, and leave some open questions. We also present some original results.Laurence Boxer, P. Christopher Staecker
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http://polipapers.upv.es/index.php/AGT/article/view/4624Mon, 03 Oct 2016 12:14:20 +0200Digital fixed points, approximate fixed points, and universal functions
http://polipapers.upv.es/index.php/AGT/article/view/4704
A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).Laurence Boxer, Ozgur Ege, Ismet Karaca, Jonathan Lopez, Joel Louwsma
Copyright (c) 2016 Applied General Topology
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http://polipapers.upv.es/index.php/AGT/article/view/4704Mon, 03 Oct 2016 12:14:21 +0200Global optimization using $\alpha$-ordered proximal contractions in metric spaces with partial orders
http://polipapers.upv.es/index.php/AGT/article/view/5180
The purpose of this article is to establish the global optimization with partial orders for the pair of non-self mappings, by introducing new type of contractions like $\alpha$-ordered contractions and $\alpha$-ordered proximal contraction in the frame work of complete metric spaces. Also calculates some fixed point theorems with the help of these generalized contractions. In addition, established an example to show the validity of our main result. These results extended and unify many existing results in the literature.<br /><br />Somayya Komal, Poom Kumam
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http://polipapers.upv.es/index.php/AGT/article/view/5180Mon, 03 Oct 2016 12:14:21 +0200Best Proximity point for Z-contraction and Suzuki type Z-contraction mappings with an application to fractional calculus
http://polipapers.upv.es/index.php/AGT/article/view/5660
In this article, we introduced the best proximity point theorems for $\mathcal{Z}$-contraction and Suzuki type $\mathcal{Z}$-contraction in the setting of complete metric spaces. Also by the help of weak $P$-property and $P$-property, we proved existence and uniqueness of best proximity point. There is a simple example to show the validity of our results. Our results extended and unify many existing results in the literature. Moreover, an application to fractional order functional differential equation is discussed.<br /><br />Somayya Komal, Poom Kumam, Dhananjay Gopal
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http://polipapers.upv.es/index.php/AGT/article/view/5660Mon, 03 Oct 2016 12:14:22 +0200Some fixed point results for dualistic rational contractions
http://polipapers.upv.es/index.php/AGT/article/view/5920
In this paper, we introduce a new contraction called dualistic contraction of rational type and obtain some fixed point results. These results generalize various comparable results appeared in the literature. We provide an example to show the superiority of our results over corresponding fixed point results proved in metric spaces.Muhammad Nazam, Muhammad Arshad, Mujahid Abbas
Copyright (c) 2016 Applied General Topology
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http://polipapers.upv.es/index.php/AGT/article/view/5920Mon, 03 Oct 2016 12:14:23 +0200