Applied General Topology - Vol 08, No 2 (2007)https://riunet.upv.es:443/handle/10251/830522021-07-31T02:34:44Z2021-07-31T02:34:44ZStone compactification of additive generalized-algebraic latticesChen, XueyouLi, QuingguoDeng, Zikehttps://riunet.upv.es:443/handle/10251/830792020-10-06T15:33:38Z2017-06-16T12:21:35ZStone compactification of additive generalized-algebraic lattices
Chen, Xueyou; Li, Quingguo; Deng, Zike
[EN] In this paper, the notions of regular, completely regular, compact additive generalized algebraic lattices are introduced, and Stone compactification is constructed. The following theorem is also obtained.
Theorem: An additive generalized algebraic lattice has a Stone compactification if and only if it is regular and completely regular.
2017-06-16T12:21:35ZLower homomorphisms on additive generalized algebraic latticesChen, XueyouDeng, Zikehttps://riunet.upv.es:443/handle/10251/830782020-10-06T15:33:38Z2017-06-16T12:18:47ZLower homomorphisms on additive generalized algebraic lattices
Chen, Xueyou; Deng, Zike
[EN] In this paper, with the additivity property, the generalized way-below relation and the maximal system of subsets as tools, we prove that all lower homomorphisms between two additive generalized algebraic lattices form an additive generalized algebraic lattice, which yields the classical theorem: the function space between T0-topological spaces is also a T0-topological space with respect to the pointwise convergence topology.
2017-06-16T12:18:47Zcl-Supercontinuous FunctionsSingh, D.https://riunet.upv.es:443/handle/10251/830772020-10-06T15:33:38Z2017-06-16T12:16:38Zcl-Supercontinuous Functions
Singh, D.
[EN] Basic properties of cl-supercontinuity, a strong variant of continuity, due to Reilly and Vamanamurthy [Indian J. Pure Appl. Math., 14 (1983), 767–772], who call such maps clopen continuous, are studied. Sufficient conditions on domain or range for a continuous function to be cl-supercontinuous are observed. Direct and inverse transfer of certain topological properties under cl-supercontinuous functions are studied and existence or nonexistence of certain cl-supercontinuous function with specified domain or range is outlined.
2017-06-16T12:16:38ZCellularity and density of balleansProtasov, Igor V.https://riunet.upv.es:443/handle/10251/830762020-10-06T15:33:38Z2017-06-16T12:14:23ZCellularity and density of balleans
Protasov, Igor V.
[EN] A ballean is a set X endowed with some family F of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. Then we define the asymptotic counterparts for dense and open subsets, introduce two cardinal invariants (density and cellularity) of balleans and prove some results concerning relationship between these invariants. We conclude the paper with applications of obtained partitions of left topological group in dense subsets.
2017-06-16T12:14:23ZOn complete accumulation points of discrete subsetsAlas, Ofelia T.Wilson, Richard G.https://riunet.upv.es:443/handle/10251/830752020-10-06T15:33:38Z2017-06-16T12:11:34ZOn complete accumulation points of discrete subsets
Alas, Ofelia T.; Wilson, Richard G.
[EN] We introduce a class of spaces in which every discretesubset has a complete accumulation point. Properties of this classare obtained and consistent examples are given to show that this classdiffers from the class of countably compact and the class of compactspaces. A number of questions are posed.
2017-06-16T12:11:34ZOn the Order Hereditary Closure Preserving Sum TheoremGong, JianhuaReilly, Ivan L.https://riunet.upv.es:443/handle/10251/830742020-10-06T15:33:38Z2017-06-16T12:05:19ZOn the Order Hereditary Closure Preserving Sum Theorem
Gong, Jianhua; Reilly, Ivan L.
[EN] The main purpose of this paper is to prove the following two theorems, an order hereditary closure preserving sum theorem and an hereditary theorem: (1) If a topological property P satisfies (Σ′) and is closed hereditary, and if V is an order hereditary closure preserving open cover of X and each V ϵ V is elementary and possesses P, then X possesses P. (2) Let a topological property P satisfy (Σ′) and (β), and be closed hereditary. Let X be a topological space which possesses P. If every open subset G of X can be written as an order hereditary closure preserving (in G) collection of elementary sets, then every subset of X possesses P.
2017-06-16T12:05:19ZCL(R) is simply connected under the Vietoris topologyEsty, N.C.https://riunet.upv.es:443/handle/10251/830732020-10-06T15:33:38Z2017-06-16T12:02:26ZCL(R) is simply connected under the Vietoris topology
Esty, N.C.
[EN] In this paper we present a proof by construction that the hyperspace CL(R) of closed, nonemtpy subsets of R is simply connected under the Vietoris topology. This is useful in considering the convergence of time scales. We also present a construction of the (known) fact that this hyperspace is also path connected, as part of the proof.
2017-06-16T12:02:26ZOn countable star-covering propertiesSong, Yan-Kuihttps://riunet.upv.es:443/handle/10251/830722020-10-06T15:33:38Z2017-06-16T11:54:57ZOn countable star-covering properties
Song, Yan-Kui
[EN] We introduce two new notions of topological spaces called a countably starcompact space and a countably absolutely countably compact (= countably acc) space. We clarify the relations between these spaces and other related spaces and investigate topological properties of countably starcompact spaces and countably acc spaces. Some examples showing the limitations of our results are also given.
2017-06-16T11:54:57ZOn br -closed setsGanster, MaximilianSteiner, Markushttps://riunet.upv.es:443/handle/10251/830712020-10-06T15:33:38Z2017-06-16T11:49:58ZOn br -closed sets
Ganster, Maximilian; Steiner, Markus
[EN] This paper is closely related to the work of Cao, Greenwood and Reilly in as it expands and completes their fundamental diagram by considering b-closed sets. In addition, we correct a wrong assertion in about βgs-spaces.
2017-06-16T11:49:58ZSandwich-type characterization of completely regular spacesGutiérrez García, JavierKubiak, Tomaszhttps://riunet.upv.es:443/handle/10251/830702021-06-25T11:14:43Z2017-06-16T11:48:07ZSandwich-type characterization of completely regular spaces
Gutiérrez García, Javier; Kubiak, Tomasz
[EN] All the higher separation axioms in topology, except for complete regularity, are known to have sandwich-type characterizations. This note provides a characterization of complete regularity in terms of inserting a continuous real-valued function. The known fact that each continuous real valued function on a compact subset o fa Tychonoff space has a continuous extension to the whole space is obtained as a corollary.
2017-06-16T11:48:07Z