Applied General Topology - Vol 06, No 1 (2005)
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Tabla de contenidos
- On functionally θ-normal spaces
- The character of free topological groups I
- The character of free topological groups II
- Abelization of join spaces of affine transformations of ordered field with proximity
- δ-closure, θ-closure and generalized closed sets
- A generalized coincidence point index
- Remarks on the finite derived set property
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- PublicationRemarks on the finite derived set property(Universitat Politècnica de València, 2005-04-01) 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.
- PublicationA generalized coincidence point index(Universitat Politècnica de València, 2005-04-01) Benkafadar, N.M.; Benkara-Mostefa, M.C.; Agence Nationale pour le Développement de la Recherche Universitaire, Argelia; Ministère de l'Enseignement Supérieur et de la Recherche Scientifique, Argelia[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.
- Publicationδ-closure, θ-closure and generalized closed sets(Universitat Politècnica de València, 2005-04-01) 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.
- PublicationAbelization of join spaces of affine transformations of ordered field with proximity(Universitat Politècnica de València, 2005-04-01) 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.
- PublicationThe character of free topological groups II(Universitat Politècnica de València, 2005-04-01) Nickolas, Peter; Tkachenko, Mikhail; Consejo Nacional de Ciencia y Tecnología, México[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.