Applied General Topology
https://riunet.upv.es:443/handle/10251/32866
2024-09-13T13:04:15ZPointwise convergence on the rings of functions which are discontinuous on a set of measure zero
https://riunet.upv.es:443/handle/10251/203797
Pointwise convergence on the rings of functions which are discontinuous on a set of measure zero
Mandal, Dhananjoy; Singha, Achintya; Bag, Sagarmoy
[EN] Consider the ring ℳ∘ ( X , μ ) of functions which are discontinuous on a set of measure zero which is introduced and studied extensively in [2]. In this paper, we have introduced a ring B1 ( X , μ ) of functions which are pointwise limits of sequences of functions in ℳ∘ ( X , μ ) . We have studied various properties of zero sets, B1 ( X , μ ) -separated and B1 ( X , μ ) -embedded subsets of B1 ( X , μ ) and also established an analogous version of Urysohn's extension theorem. We have investigated a connection between ideals of B1 ( X , μ ) and ZB -filters on X. We have studied an analogue of Gelfand-Kolmogoroff theorem in our setting. We have defined real maximal ideals of B1 ( X , μ ) and established the result | ℛ M a x ( ℳ∘ ( X , μ ) ) | = | ℛ M a x ( B1 ( X , μ ) ) | , where ℛ M a x ( ℳ∘ ( X , μ ) ) and ℛ M a x ( B1 ( X , μ ) ) are the sets of all real maximal ideals of ℳ∘ ( X , μ ) and B1 ( X , μ ) respectively.
2024-04-26T12:40:58ZStrongly Lipschitz (ℓp ,ℓq)-factorable mappings
https://riunet.upv.es:443/handle/10251/203796
Strongly Lipschitz (ℓp ,ℓq)-factorable mappings
Achour, Dahmane; Tiaiba, Toufik
[EN] In this paper we study the space of strongly Lipschitz (ℓp, ℓq) -factorable operators between metric spaces and a Banach spaces. In particular, a factorization of this class through ℓp and ℓq spaces is given. We show that this type of operators fits in the theory of composition α-Banach Lipschitz operator ideal. As a special case, we get a Lipschitz version of weakly p-nuclear operators.
2024-04-26T12:35:34ZOn topological groups of monotonic automorphisms
https://riunet.upv.es:443/handle/10251/203795
On topological groups of monotonic automorphisms
Buzyakova, Raushan
[EN] We study topological groups of monotonic automorphisms on a generalized ordered space L. We find a condition that is necessary and sufficient for the set of all monotonic automorphism on L along with the function composition and the topology of point-wise convergence to be a topological group.
2024-04-26T12:25:42ZThe degree of nondensifiability of linear bounded operators and its applications
https://riunet.upv.es:443/handle/10251/203794
The degree of nondensifiability of linear bounded operators and its applications
García, Gonzalo; Mora, Gaspar
[EN] In the present paper we define the degree of nondensifiability (DND for short) of a bounded linear operator T on a Banach space and analyze its properties and relations with the Hausdorff measure of non-compactness (MNC for short) of T. As an application of our results, we have obtained a formula to find the essential spectral radius of a bounded operator T on a Banach space as well as we have provided the best possible lower bound for the Hyers-Ulam stability constant of T in terms of the aforementioned DND.
2024-04-26T12:23:39ZCompactness in the endograph uniformity
https://riunet.upv.es:443/handle/10251/203793
Compactness in the endograph uniformity
Sánchez, Iván
[EN] Given a uniform space (X,U), we denote by F*(X) to the family of fuzzy sets u in (X,U) such that u is normal and upper semicontinuous. Let UE be the endograph uniformity on F*(X). In this paper, we mainly characterize totally bounded and compact substes in the uniform space (F*(X),UE).
2024-04-26T12:21:15ZA study of new dimensions for ideal topological spaces
https://riunet.upv.es:443/handle/10251/203792
A study of new dimensions for ideal topological spaces
Sereti, Fotini
[EN] In this paper new notions of dimensions for ideal topological spaces are inserted, called *-quasi covering dimension and ideal quasicovering dimension. We study several of their properties and investigate their relations with types of covering dimensions like the *-covering dimension and the ideal covering dimension.
2024-04-26T12:14:29ZHemi metric spaces and Banach fixed point theorems
https://riunet.upv.es:443/handle/10251/203791
Hemi metric spaces and Banach fixed point theorems
Ozturk, Vildan; Radenovic, Stojan
[EN] In this work, we will define a new type metric with degree m and m+1 points which is called m-hemi metric as a generalization of two metric spaces. We will give and prove some topological properties. Also, Banach contraction mapping principle were proved and a application to Fredholm integral equation were gived in hemi metric spaces.
2024-04-26T12:12:16ZSome existence and uniqueness results for a solution of a system of equations
https://riunet.upv.es:443/handle/10251/203790
Some existence and uniqueness results for a solution of a system of equations
Khantwal, Deepak; Pant, Rajendra
[EN] This paper presents some existence and uniqueness results for a solution of a system of equations. Our results extend and generalize the well-known and celebrated results of Boyd and Wong [Proc. Amer. Math. Soc. 20 (1969)], Matkowski [Dissertations Math.(Rozprawy Mat.) 127 (1975)], Proinov [Nonlinear Anal. 64 (2006)], Ri [Indag. Math. (N. S.) 27 (2016)] and many others. We also present some illustrative examples to validate our results.
2024-04-26T12:08:39ZPartial actions of groups on profinite spaces
https://riunet.upv.es:443/handle/10251/203789
Partial actions of groups on profinite spaces
Martínez, Luis; Tapia, Héctor Pinedo; Villamizar, Andrés
[EN] We show that for a partial action η with closed domain of a compact group G on a profinite space X the space of orbits X/~G is profinite, this leads to the fact that when G is profinite the enveloping space XG is also profinite. Moreover, we provide conditions for the induced quotient map πG : X → X / ∼G of η to have a continuous section. Relations between continuous sections of πG and continuous sections of the quotient map induced by the enveloping action of η are also considered. At the end of this work, we prove that the category of actions on profinite spaces with countable number of clopen sets is reflective in the category of actions of compact Hausdorff spaces having countable number of clopen sets.
2024-04-26T12:01:45ZPartial actions on quotient spaces and globalization
https://riunet.upv.es:443/handle/10251/203788
Partial actions on quotient spaces and globalization
Martínez, Luis; Tapia, Héctor Pinedo; Villamizar, Andrés
[EN] Given a partial action of a topological group G on a topological space X we determine properties P which can be extended from X to its globalization. We treat the cases when P is any of the following: Hausdorff, regular, metrizable, second countable and having invariant metric. Further, for a normal subgroup H, we introduce and study a partial actionof G/H on the orbit space X/∼H, applications to invariant metric sand inverse limits are presented.
2024-04-26T11:58:15Z