Gong, Jianhua; Reilly, Ivan L.(Universitat Politècnica de València, 2007-10-01)
[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, ...
Esty, N.C.(Universitat Politècnica de València, 2007-10-01)
[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. ...
Song, Yan-Kui(Universitat Politècnica de València, 2007-10-01)
[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 ...
Ganster, Maximilian; Steiner, Markus(Universitat Politècnica de València, 2007-10-01)
[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.
Gutiérrez García, Javier; Kubiak, Tomasz(Universitat Politècnica de València, 2007-10-01)
[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 ...