Applied General Topology - Vol 21, No 1 (2020)

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https://riunet.upv.es/handle/10251/141532

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Topological characterizations of amenability and congeniality of bases
Dynamic properties of the dynamical system SFnm(X), SFnm(f))
On a metric of the space of idempotent probability measures
Counterexample of theorems on star versions of Hurewicz property
Existence of Picard operator and iterated function system
New topologies between the usual and Niemytzki
A note on rank 2 diagonals
Fixed poin sets in digital topology, 1
Fixed point sets in digital topology, 2
Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces
Selection principles and covering properties in bitopological spaces

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Now showing 1 - 5 of 11

Topological characterizations of amenability and congeniality of bases
(Universitat Politècnica de València, 2020-04-03) López-Permouth, Sergio R.; Stanley, Benjamin
[EN] 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.A basis B over an innite dimensional F-algebra A is called amenable if FB, 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.(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.
Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces
(Universitat Politècnica de València, 2020-04-03) Okeke, Godwin Amechi; Abbas, Mujahid; Abdus Salam School of Mathematical Sciences
[EN] 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.
Existence of Picard operator and iterated function system
(Universitat Politècnica de València, 2020-04-03) Garg, Medha; Chandok, Sumit; Department of Science and Technology, Ministry of Science and Technology, India
[EN] In this paper, we define weak θm− 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 θm− iterated multifunction system. Moreover, we introduce (α, β, θm)− 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.
Fixed poin sets in digital topology, 1
(Universitat Politècnica de València, 2020-04-03) Boxer, Laurence; Staecker, P. Christopher
[EN] 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. 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(Cn) where Cn 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 Cn, in which F(X) does not equal {0, 1, . . . , #X}. 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.
New topologies between the usual and Niemytzki
(Universitat Politècnica de València, 2020-04-03) Abuzaid, Dina; Alqahtani, Maha; Kalantan, Lutfi
[EN] 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.

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