Applied General Topology - Vol 20, No 1 (2019)
https://riunet.upv.es:443/handle/10251/118953
2020-02-18T09:26:11ZExtremal balleans
https://riunet.upv.es:443/handle/10251/118978
Extremal balleans
Protasov, Igor
[EN] A ballean (or coarse space) is a set endowed with a coarse structure. A ballean X is called normal if any two asymptotically disjoint subsets of X are asymptotically separated. We say that a ballean X is ultra-normal (extremely normal) if any two unbounded subsets of X are not asymptotically disjoint (every unbounded subset of X is large). Every maximal ballean is extremely normal and every extremely normal ballean is ultranormal, but the converse statements do not hold. A normal ballean is ultranormal if and only if the Higson′s corona of X is a singleton. A discrete ballean X is ultranormal if and only if X is maximal. We construct a series of concrete balleans with extremal properties.
2019-04-04T10:29:43ZExistence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces
https://riunet.upv.es:443/handle/10251/118977
Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces
Pant, Rajendra; Pandey, Rameshwa
[EN] We consider a wider class of nonexpansive type mappings and present some fixed point results for this class of mappingss in hyperbolic spaces. Indeed, first we obtain some existence results for this class of mappings. Next, we present some convergence results for an iteration algorithm for the same class of mappings. Some illustrative non-trivial examples have also been discussed.
2019-04-04T10:25:02ZA quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications
https://riunet.upv.es:443/handle/10251/118976
A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications
García, G.
[EN] We present a novel result that, in a certain sense, generalizes the Arzelà-Ascoli theorem. Our main tool will be the so called degree of nondensifiability, which is not a measure of noncompactness but canbe used as an alternative tool in certain fixed problems where such measures do not work out. To justify our results, we analyze the existence of continuous solutions of certain Volterra integral equations defined by vector valued functions.
2019-04-04T10:20:47ZExact computation for existence of a knot counterexample
https://riunet.upv.es:443/handle/10251/118975
Exact computation for existence of a knot counterexample
Marinelli, K.; Peters, T. J.
[EN] Previously, numerical evidence was presented of a self-intersecting Bezier curve having the unknot for its control polygon. This numerical demonstration resolved open questions in scientic visualization, but did not provide a formal proof of self-intersection. An example with a formal existence proof is given, even while the exact self-intersection point remains undetermined.
2019-04-04T10:13:01ZOn rings of Baire one functions
https://riunet.upv.es:443/handle/10251/118974
On rings of Baire one functions
Deb Ray, A.; Mondal, Atanu
[EN] This paper introduces the ring of all real valued Baire one functions, denoted by B1(X) and also the ring of all real valued bounded Baire one functions, denoted by B∗1(X). Though the resemblance between C(X) and B1(X) is the focal theme of this paper, it is observed that unlike C(X) and C∗(X) (real valued bounded continuous functions), B∗1 (X) is a proper subclass of B1(X) in almost every non-trivial situation. Introducing B1-embedding and B∗1-embedding, several analogous results, especially, an analogue of Urysohn’s extension theorem is established.
2019-04-04T10:08:09ZWhen is the super socle of C(X) prime?
https://riunet.upv.es:443/handle/10251/118973
When is the super socle of C(X) prime?
Ghasemzadeh, S.; Namdari, M.
[EN] Let SCF(X) denote the ideal of C(X) consisting of functions which are zero everywhere except on a countable number of points of X. It is generalization of the socle of C(X) denoted by CF(X). Using this concept we extend some of the basic results concerning CF(X) to SCF(X). In particular, we characterize the spaces X such that SCF(X) is a prime ideal in C(X) (note, CF(X) is never a prime ideal in C(X)). This may be considered as an advantage of SCF(X) over C(X). We are also interested in characterizing topological spaces X such that Cc(X) =R+SCF(X), where Cc(X) denotes the subring of C(X) consisting of functions with countable image.
2019-04-04T09:59:34ZA non-discrete space X with Cp(X) Menger at infinity
https://riunet.upv.es:443/handle/10251/118972
A non-discrete space X with Cp(X) Menger at infinity
Bella, Angelo; Hernández-Gutiérrez, Rodrigo
[EN] In a paper by Bella, Tokgös and Zdomskyy it is asked whether there exists a Tychonoff space X such that the remainder of Cp(X) in some compactification is Menger but not σ-compact. In this paper we prove that it is consistent that such space exists and in particular its existence follows from the existence of a Menger ultrafilter.
2019-04-04T09:54:40ZGeneric theorems in the theory of cardinal invariants of topological spaces
https://riunet.upv.es:443/handle/10251/118971
Generic theorems in the theory of cardinal invariants of topological spaces
Ramírez-Páramo, Alejandro; Tenorio, Jesús F.
[EN] The main aim of this paper is to present a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related. Moreover, we use this result and the weak Hausdorff number, H∗, introduced by Bonanzinga in [Houston J. Math. 39 (3) (2013), 1013–1030], to generalize some upper bounds on the cardinality of topological spaces.
2019-04-04T09:42:24ZA viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space
https://riunet.upv.es:443/handle/10251/118970
A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space
Izuchukwu, C.; Aremu, K. O.; Mebawondu, A. A.; Mewomo, O. T.
[EN] The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces.
2019-04-04T09:38:52ZCauchy action on filter spaces
https://riunet.upv.es:443/handle/10251/118969
Cauchy action on filter spaces
Rath, N.
[EN] A Cauchy group (G,D,·) has a Cauchy-action on a filter space (X,C), if it acts in a compatible manner. A new filter-based method is proposed in this paper for the notion of group-action, from which the properties of this action such as transitiveness and its compatibility with various modifications of the G-space (X,C) are determined. There is a close link between the Cauchy action and the induced continuous action on the underlying G-space, which is explored here. In addition, a possible extension of a Cauchy-action to the completion of the underlying G-space is discussed. These new results confirm and generalize some of the properties of group action in a topological context.
2019-04-04T09:34:37Z