Applied General Topology - Vol 06, No 1 (2005)
https://riunet.upv.es:443/handle/10251/82600
Tue, 23 Apr 2024 16:54:27 GMT2024-04-23T16:54:27ZRemarks on the finite derived set property
https://riunet.upv.es:443/handle/10251/82627
Remarks on the finite derived set property
Bella, Angelo
[EN] The finite derived set property asserts that any infinite subset of a space has an infinite subset with only finitely many accumulation points. Among other things, we study this property in the case of a function space with the topology of pointwise convergence.
Fri, 09 Jun 2017 07:42:12 GMThttps://riunet.upv.es:443/handle/10251/826272017-06-09T07:42:12ZA generalized coincidence point index
https://riunet.upv.es:443/handle/10251/82626
A generalized coincidence point index
Benkafadar, N.M.; Benkara-Mostefa, M.C.
[EN] The paper is devoted to build for some pairs of continuous single-valued maps a coincidence point index. The class of pairs (f, g) satisfies the condition that f induces an epimorphism of the Cech homology groups with compact supports and coefficients in the field of rational numbers Q. Using this concept one defines for a class of multi-valued mappings a fixed point degree. The main theorem states that if the general coincidence point index is different from {0}, then the pair (f, g) admits at least a coincidence point. The results may be considered as a generalization of the above Eilenberg-Montgomery theorems [12], they include also, known fixed-point and coincidence-point theorems for single-valued maps and multi-valued transformations.
Fri, 09 Jun 2017 07:40:26 GMThttps://riunet.upv.es:443/handle/10251/826262017-06-09T07:40:26Zδ-closure, θ-closure and generalized closed sets
https://riunet.upv.es:443/handle/10251/82624
δ-closure, θ-closure and generalized closed sets
Cao, Jiling; Ganster, Maximilian; Reilly, Ivan L.; Steiner, Markus
[EN] We study some new classes of generalized closed sets (in the sense of N. Levine) in a topological space via the associated δ-closure and θ-closure. The relationships among these new classes and existing classes of generalized closed sets are investigated. In the last section we provide an extensive and more or less complete survey on separation axioms characterized via singletons.
Fri, 09 Jun 2017 07:36:32 GMThttps://riunet.upv.es:443/handle/10251/826242017-06-09T07:36:32ZAbelization of join spaces of affine transformations of ordered field with proximity
https://riunet.upv.es:443/handle/10251/82623
Abelization of join spaces of affine transformations of ordered field with proximity
Hosková, Sárka
[EN] Using groups of affine transformations of linearly ordered fields a certain construction of non-commutative join hypergroups is presented based on the criterion of reproducibility of semi-hypergroups which are determined by ordered semigroups. The aim of this paper is to construct the abelization of the non-commutative join space of affine transformations of ordered fields. A construction of commutative weakly associative hypergroup (Hv-group) is made and a proximity is defined on this structure.
Fri, 09 Jun 2017 07:34:01 GMThttps://riunet.upv.es:443/handle/10251/826232017-06-09T07:34:01ZThe character of free topological groups II
https://riunet.upv.es:443/handle/10251/82622
The character of free topological groups II
Nickolas, Peter; Tkachenko, Mikhail
[EN] A systematic analysis is made of the character of the free and free abelian topological groups on metrizable spaces and compact spaces, and on certain other closely related spaces. In the first case, it is shown that the characters of the free and the free abelian topological groups on X are both equal to the “small cardinal” d if X is compact and metrizable, but also, more generally, if X is a non-discrete k!-space all of whose compact subsets are metrizable, or if X is a non-discrete Polish space. An example is given of a zero-dimensional separable metric space for which both characters are equal to the cardinal of the continuum. In the case of a compact space X, an explicit formula is derived for the character of the free topological group on X involving no cardinal invariant of X other than its weight; in particular the character is fully determined by the weight in the compact case. This paper is a sequel to a paper by the same authors in which the characters of the free groups were analysed under less restrictive topological assumptions.
Fri, 09 Jun 2017 07:29:27 GMThttps://riunet.upv.es:443/handle/10251/826222017-06-09T07:29:27ZThe character of free topological groups I
https://riunet.upv.es:443/handle/10251/82621
The character of free topological groups I
Nickolas, Peter; Tkachenko, Mikhail
[EN] A systematic analysis is made of the character of the free and free abelian topological groups on uniform spaces and on topological spaces. In the case of the free abelian topological group on a uniform space, expressions are given for the character in terms of simple cardinal invariants of the family of uniformly continuous pseudometrics of the given uniform space and of the uniformity itself. From these results, others follow on the basis of various topological assumptions. Amongst these: (i) if X is a compact Hausdorff space, then the character of the free abelian topological group on X lies between w(X) and w(X)ℵ0, where w(X) denotes the weight of X; (ii) if the Tychonoff space X is not a P-space, then the character of the free abelian topological group is bounded below by the “small cardinal” d; and (iii) if X is an infinite compact metrizable space, then the character is precisely d. In the non-abelian case, we show that the character of the free abelian topological group is always less than or equal to that of the corresponding free topological group, but the inequality is in general strict. It is also shown that the characters of the free abelian and the free topological groups are equal whenever the given uniform space is w-narrow. A sequel to this paper analyses more closely the cases of the free and free abelian topological groups on compact Hausdorff spaces and metrizable spaces.
Fri, 09 Jun 2017 07:23:37 GMThttps://riunet.upv.es:443/handle/10251/826212017-06-09T07:23:37ZOn functionally θ-normal spaces
https://riunet.upv.es:443/handle/10251/82620
On functionally θ-normal spaces
Kohli, J.K.; Das, A.K.
[EN] Characterizations of functionally θ-normal spaces including the one that of Urysohn’s type lemma, are obtained. Interrelations among (functionally) θ-normal spaces and certain generalizations of normal spaces are discussed. It is shown that every almost regular (or mildly normal ≡ k-normal) θ-normal space is functionally θ-normal. Moreover, it is shown that every almost regular weakly θ-normal space is mildly normal. A factorization of functionally θ-normal space is given. A Tietze’s type theorem for weakly functionally θ-normal space is obtained. A variety of situations in mathematical literature wherein the spaces encountered are (functionally) θ-normal but not normal are illustrated.
Fri, 09 Jun 2017 07:17:24 GMThttps://riunet.upv.es:443/handle/10251/826202017-06-09T07:17:24Z