Applied General Topology
https://polipapers.upv.es/index.php/AGT
<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>Universitat Politècnica de Valènciaen-USApplied General Topology1576-9402The 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>Topological characterizations of amenability and congeniality of bases
https://polipapers.upv.es/index.php/AGT/article/view/11488
<div>We provide topological interpretations of the recently introduced notions of amenability and congeniality of bases of innite dimensional algebras. In order not to restrict our attention only to the countable dimension case, the uniformity of the topologies involved is analyzed and therefore the pertinent ideas about uniform topological spaces are surveyed.</div><div><p>A basis B over an innite dimensional F-algebra A is called amenable if F<sup>B</sup>, the direct product indexed by B of copies of the eld F, can be made into an A-module in a natural way. (Mutual) congeniality is a relation that serves to identify cases when different amenable bases yield isomorphic A-modules.</p><p>(Not necessarily mutual) congeniality between amenable bases yields an epimorphism of the modules they induce. We prove that this epimorphism is one-to-one only if the congeniality is mutual, thus establishing a precise distinction between the two notions.</p></div>Sergio R. López-PermouthBenjamin Stanley
Copyright (c) 2020 Applied General Topology
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2020-04-032020-04-0321111510.4995/agt.2020.11488Dynamic properties of the dynamical system SFnm(X), SFnm(f))
https://polipapers.upv.es/index.php/AGT/article/view/11807
<p>Let X be a continuum and let n be a positive integer. We consider the hyperspaces F<sub>n</sub>(X) and SF<sub>n</sub>(X). If m is an integer such that n > m ≥ 1, we consider the quotient space SF<sup>n</sup><sub>m</sub>(X). For a given map f : X → X, we consider the induced maps F<sub>n</sub>(f) : F<sub>n</sub>(X) → F<sub>n</sub>(X), SF<sub>n</sub>(f) : SF<sub>n</sub>(X) → SF<sub>n</sub>(X) and SF<sup>n</sup><sub>m</sub>(f) : SF<sup>n</sup><sub>m</sub>(X) → SF<sup>n</sup><sub>m</sub>(X). In this paper, we introduce the dynamical system (SF<sup>n</sup><sub>m</sub>(X), SF<sup>n</sup><sub>m</sub> (f)) and we investigate some relationships between the dynamical systems (X, f), (F<sub>n</sub>(X), F<sub>n</sub>(f)), (SF<sub>n</sub>(X), SF<sub>n</sub>(f)) and (SF<sup>n</sup><sub>m</sub>(X), SF<sup>n</sup><sub>m</sub>(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.</p>Franco BarragánAlicia Santiago-SantosJesús F. Tenorio
Copyright (c) 2020 Applied General Topology
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2020-04-032020-04-03211173410.4995/agt.2020.11807On a metric of the space of idempotent probability measures
https://polipapers.upv.es/index.php/AGT/article/view/11865
<p>In this paper we introduce a metric on the space I(X) of idempotent probability measures on a given compact metric space (X; ρ), which extends the metric ρ. It is proven the introduced metric generates the pointwise convergence topology on I(X).</p>Adilbek Atakhanovich Zaitov
Copyright (c) 2020 Applied General Topology
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2020-04-032020-04-03211355110.4995/agt.2020.11865Counterexample of theorems on star versions of Hurewicz property
https://polipapers.upv.es/index.php/AGT/article/view/11976
In this paper, an example contradicting Theorem 4.5 and Theorem 5.3 is provided and these theorems are proved under some extra hypothesis.Manoj Bhardwaj
Copyright (c) 2020 Applied General Topology
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2020-04-032020-04-03211535610.4995/agt.2020.11976Existence of Picard operator and iterated function system
https://polipapers.upv.es/index.php/AGT/article/view/11992
<p>In this paper, we define weak θ<sub>m</sub>− contraction mappings and give a new class of Picard operators for such class of mappings on a complete metric space. Also, we obtain some new results on the existence and uniqueness of attractor for a weak θ<sub>m</sub>− iterated multifunction system. Moreover, we introduce (α, β, θ<sub>m</sub>)− contractions using cyclic (α, β)− admissible mappings and obtain some results for such class of mappings without the continuity of the operator. We also provide an illustrative example to support the concepts and results proved herein.</p>Medha GargSumit Chandok
Copyright (c) 2020 Applied General Topology
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2020-04-032020-04-03211577010.4995/agt.2020.11992New topologies between the usual and Niemytzki
https://polipapers.upv.es/index.php/AGT/article/view/12042
We use the technique of Hattori to generate new topologies on the closed upper half plane which lie between the usual metric topology and the Niemytzki topology. We study some of their fundamental properties and weaker versions of normality.Dina AbuzaidMaha AlqahtaniLutfi Kalantan
Copyright (c) 2020 Applied General Topology
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2020-04-032020-04-03211717910.4995/agt.2020.12042A note on rank 2 diagonals
https://polipapers.upv.es/index.php/AGT/article/view/12065
<p>We solve two questions regarding spaces with a (G<sub>δ</sub>)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos about weakly Lindelöf spaces with a G<sub>δ</sub>-diagonal of rank 2 and the other is a question of Arhangel’skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.</p>Angelo BellaSanti Spadaro
Copyright (c) 2020 Applied General Topology
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2020-04-032020-04-03211818510.4995/agt.2020.12065Fixed poin sets in digital topology, 1
https://polipapers.upv.es/index.php/AGT/article/view/12091
<p>In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results that often differ greatly from standard results in classical topology.</p><p>We introduce several measures related to fixed points for continuous self-maps on digital images, and study their properties. Perhaps the most important of these is the fixed point spectrum F(X) of a digital image: that is, the set of all numbers that can appear as the number of fixed points for some continuous self-map. We give a complete computation of F(C<sub>n</sub>) where C<sub>n</sub> is the digital cycle of n points. For other digital images, we show that, if X has at least 4 points, then F(X) always contains the numbers 0, 1, 2, 3, and the cardinality of X. We give several examples, including C<sub>n</sub>, in which F(X) does not equal {0, 1, . . . , #X}.</p><p>We examine how fixed point sets are affected by rigidity, retraction, deformation retraction, and the formation of wedges and Cartesian products. We also study how fixed point sets in digital images can be arranged; e.g., for some digital images the fixed point set is always connected.</p>Laurence BoxerP. Christopher Staecker
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2020-04-032020-04-032118711010.4995/agt.2020.12091Fixed point sets in digital topology, 2
https://polipapers.upv.es/index.php/AGT/article/view/12101
We continue the work of [10], studying properties of digital images determined by fixed point invariants. We introduce pointed versions of invariants that were introduced in [10]. We introduce freezing sets and cold sets to show how the existence of a fixed point set for a continuous self-map restricts the map on the complement of the fixed point set.Laurence Boxer
Copyright (c) 2020 Applied General Topology
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2020-04-032020-04-0321111113310.4995/agt.2020.12101Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces
https://polipapers.upv.es/index.php/AGT/article/view/12220
It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.Godwin Amechi OkekeMujahid Abbas
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2020-04-032020-04-0321113515810.4995/agt.2020.12220Selection principles and covering properties in bitopological spaces
https://polipapers.upv.es/index.php/AGT/article/view/12238
<p>Our main focus in this paper is to introduce and study various selection principles in bitopological spaces. In particular, Menger type, and Hurewicz type covering properties like: Almost p-Menger, star p-Menger, strongly star p-Menger, weakly p-Hurewicz, almost p-Hurewicz, star p-Hurewicz and strongly star p-Hurewicz spaces are defined and corresponding properties are investigated. Relations between some of these spaces are established.</p>Moiz ud Din KhanAmani Sabah
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2020-04-032020-04-0321115916910.4995/agt.2020.12238