Applied General Topology - Vol 21, No 1 (2020)
https://riunet.upv.es:443/handle/10251/141532
2021-08-05T08:23:58ZTopological characterizations of amenability and congeniality of bases
https://riunet.upv.es:443/handle/10251/141567
Topological characterizations of amenability and congeniality of bases
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.
2020-04-27T09:39:25ZFejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces
https://riunet.upv.es:443/handle/10251/141565
Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces
Okeke, Godwin Amechi; Abbas, Mujahid
[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.
2020-04-27T09:31:40ZExistence of Picard operator and iterated function system
https://riunet.upv.es:443/handle/10251/141559
Existence of Picard operator and iterated function system
Garg, Medha; Chandok, Sumit
[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.
2020-04-27T09:18:29ZFixed poin sets in digital topology, 1
https://riunet.upv.es:443/handle/10251/141555
Fixed poin sets in digital topology, 1
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.
2020-04-27T09:09:27ZNew topologies between the usual and Niemytzki
https://riunet.upv.es:443/handle/10251/141554
New topologies between the usual and Niemytzki
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.
2020-04-27T09:06:03ZCounterexample of theorems on star versions of Hurewicz property
https://riunet.upv.es:443/handle/10251/141553
Counterexample of theorems on star versions of Hurewicz property
Bhardwaj, Manoj
[EN] In this paper, an example contradicting Theorem 4.5 and Theorem 5.3 is provided and these theorems are proved under some extra hypothesis.
2020-04-27T09:04:32ZDynamic properties of the dynamical system SFnm(X), SFnm(f))
https://riunet.upv.es:443/handle/10251/141550
Dynamic properties of the dynamical system SFnm(X), SFnm(f))
Barragán, Franco; Santiago-Santos, Alicia; Tenorio, Jesús F.
[EN] Let X be a continuum and let n be a positive integer. We consider the hyperspaces Fn(X) and SFn(X). If m is an integer such that n > m ≥ 1, we consider the quotient space SFnm(X). For a given map f : X → X, we consider the induced maps Fn(f) : Fn(X) → Fn(X), SFn(f) : SFn(X) → SFn(X) and SFnm(f) : SFnm(X) → SFnm(X). In this paper, we introduce the dynamical system (SFnm(X), SFnm (f)) and we investigate some relationships between the dynamical systems (X, f), (Fn(X), Fn(f)), (SFn(X), SFn(f)) and (SFnm(X), SFnm(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.
2020-04-27T09:01:00ZSelection principles and covering properties in bitopological spaces
https://riunet.upv.es:443/handle/10251/141549
Selection principles and covering properties in bitopological spaces
Khan, Moiz ud Din; Sabah, Amani
[EN] 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.
2020-04-27T08:51:17ZA note on rank 2 diagonals
https://riunet.upv.es:443/handle/10251/141548
A note on rank 2 diagonals
Bella, Angelo; Spadaro, Santi
[EN] We solve two questions regarding spaces with a (Gδ)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos about weakly Lindelöf spaces with a Gδ-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.
2020-04-27T08:46:53ZFixed point sets in digital topology, 2
https://riunet.upv.es:443/handle/10251/141546
Fixed point sets in digital topology, 2
Boxer, Laurence
[EN] 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.
2020-04-27T08:39:50Z