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Keywords = hemicompact space

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10 pages, 284 KB  
Article
Baire 1 Functions and the Topology of Uniform Convergence on Compacta
by Ľubica Holá and Dušan Holý
Mathematics 2024, 12(10), 1494; https://doi.org/10.3390/math12101494 - 10 May 2024
Viewed by 1608
Abstract
Let X be a Tychonoff topological space, B1(X,R) be the space of real-valued Baire 1 functions on X and τUC be the topology of uniform convergence on compacta. The main purpose of this paper is [...] Read more.
Let X be a Tychonoff topological space, B1(X,R) be the space of real-valued Baire 1 functions on X and τUC be the topology of uniform convergence on compacta. The main purpose of this paper is to study cardinal invariants of (B1(X,R),τUC). We prove that the following conditions are equivalent: (1) (B1(X,R),τUC) is metrizable; (2) (B1(X,R),τUC) is completely metrizable; (3) (B1(X,R),τUC) is Čech-complete; and (4) X is hemicompact. It is also proven that if X is a separable metric space with a non isolated point, then the topology of uniform convergence on compacta on B1(X,R) is seen to behave like a metric topology in the sense that the weight, netweight, density, Lindelof number and cellularity are all equal for this topology and they are equal to c= |B1(X,R)|. We find further conditions on X under which these cardinal invariants coincide on B1(X,R). Full article
(This article belongs to the Section B: Geometry and Topology)
16 pages, 307 KB  
Article
Approximation of the Solution of Split Equality Fixed Point Problem for Family of Multivalued Demicontractive Operators with Application
by Ismat Beg, Mujahid Abbas and Muhammad Waseem Asghar
Mathematics 2023, 11(4), 959; https://doi.org/10.3390/math11040959 - 13 Feb 2023
Cited by 2 | Viewed by 1819
Abstract
In this paper, a new viscosity type iterative algorithm is used for obtaining a strong convergence result of split equality fixed point solutions for infinite families of multivalued demicontractive mappings in real Hilbert spaces. Our iterative scheme is based on choosing the step-sizes [...] Read more.
In this paper, a new viscosity type iterative algorithm is used for obtaining a strong convergence result of split equality fixed point solutions for infinite families of multivalued demicontractive mappings in real Hilbert spaces. Our iterative scheme is based on choosing the step-sizes without calculating or estimating the operator norms and the condition of hemicompactness was relaxed to prove the strong convergence result. As an application, the solution of split convex minimization problem was approximated. The result presented herein unifies and extends several comparable results in the literature. Full article
7 pages, 305 KB  
Article
Classifying Topologies through G-Bases
by Juan Carlos Ferrando and Manuel López-Pellicer
Axioms 2022, 11(12), 744; https://doi.org/10.3390/axioms11120744 - 19 Dec 2022
Cited by 1 | Viewed by 2231
Abstract
We classify several topological properties of a Tychonoff space X by means of certain locally convex topologies T with a G-base located between the pointwise topology τp and the bounded-open topology τb of the real-valued continuous function space CX [...] Read more.
We classify several topological properties of a Tychonoff space X by means of certain locally convex topologies T with a G-base located between the pointwise topology τp and the bounded-open topology τb of the real-valued continuous function space CX. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications III)
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