Applied General Topology - Vol 10, No 2 (2009)https://riunet.upv.es:443/handle/10251/866972020-01-22T02:28:15Z2020-01-22T02:28:15ZUniformizable and realcompact bornological universesVroegrijk, Tomhttps://riunet.upv.es:443/handle/10251/867092019-12-17T07:13:05Z2017-09-07T12:09:18ZUniformizable and realcompact bornological universes
Vroegrijk, Tom
[EN] Bornological universes were introduced some time ago by Hu and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces and optimization theory. One o fHu's results gives us a necessary and sufficient condition for which a bornological universe is metrizable. In this article we will extend thi sresult and give a characterization of uniformizable bornological universes. Furthermore, a construction on bornological universes that the author used to find the bornological dual of function spaces endowed with the bounded-open topology will be used to define realcompactness for bornological universes. We will also give various characterizations of this new concept.
2017-09-07T12:09:18ZCompact self T1-complementary spaces without isolated pointsTkachenko, Mikhailhttps://riunet.upv.es:443/handle/10251/867082019-12-02T22:04:13Z2017-09-07T12:07:01ZCompact self T1-complementary spaces without isolated points
Tkachenko, Mikhail
[EN] We present an example of a compact Hausdorff self T1-complementary space without isolated points. This answers Question 3.11 from [A compact Hausdorff topology that is a T1-complementof itself, Fund. Math. 175 (2002), 163–173] affirmatively.
2017-09-07T12:07:01ZMichael spaces and Dowker planksCaserta, AgataWatson, Stephenhttps://riunet.upv.es:443/handle/10251/867072019-12-02T22:04:13Z2017-09-07T12:04:54ZMichael spaces and Dowker planks
Caserta, Agata; Watson, Stephen
[EN] We investigate the Lindelöf property of Dowker planks. In particular, we give necessary conditions such that the product of a Dowker plank with the irrationals is not Lindelöf. We also show that if there exists a Michael space, then, under some conditions involving singular cardinals, there is one that is a Dowker plank.
2017-09-07T12:04:54ZAlmost periodic points and minimal sets in topological spacesFujita, ChikaraKato, Hisaohttps://riunet.upv.es:443/handle/10251/867062019-12-02T22:04:13Z2017-09-07T12:02:30ZAlmost periodic points and minimal sets in topological spaces
Fujita, Chikara; Kato, Hisao
[EN] In the paper [Almost periodic points and minimal sets in w-regular spaces, Topology Appl. 154 (2007), 2873–2879], Mai and Sun showed that several known results concerning almost periodic points and minimal sets of maps can be generalized from regular spaces to w-regular spaces. Also, they have three unsolved problems. In this paper, we answer to all problems which remain unsolved in the paper of Mai and Sun. In fact we prove some general theorems which give counte rexamples of the problems.
2017-09-07T12:02:30ZQuasihomeomorphisms and lattice equivalent topological spacesEchi, OthmanLazaar, Samihttps://riunet.upv.es:443/handle/10251/867052019-12-02T22:04:14Z2017-09-07T11:58:24ZQuasihomeomorphisms and lattice equivalent topological spaces
Echi, Othman; Lazaar, Sami
[EN] This paper deals with lattice-equivalence of topologica lspaces. We are concerned with two questions: the first one is when two topological spaces are lattice equivalent; the second one is what additional conditions have to be imposed on lattice equivalent spaces in order that they be homeomorphic. We give a contribution to the study of these questions. Many results of Thron [Lattice-equivalence of topological spaces, Duke Math. J. 29 (1962), 671-679] are recovered, clarified and commented.
2017-09-07T11:58:24ZOn an algebraic version of Tamano’s theoremBuzyakova, Raushan Z.https://riunet.upv.es:443/handle/10251/867032019-12-02T22:04:14Z2017-09-07T11:48:45ZOn an algebraic version of Tamano’s theorem
Buzyakova, Raushan Z.
[EN] Let X be a non-paracompact subspace of a linearly ordered topological space. We prove, in particular, that if a Hausdorff topological group G contains closed copies of X and a Hausdorff compactification bX of X then G is not normal. The theorem also holds in the class of monotonically normal spaces.
2017-09-07T11:48:45ZMore on ultrafilters and topological gamesGonzález-Silva, R.A.Hrusák, M.https://riunet.upv.es:443/handle/10251/867022019-12-02T22:04:14Z2017-09-07T11:44:11ZMore on ultrafilters and topological games
González-Silva, R.A.; Hrusák, M.
[EN] Two different open-point games are studied here, the G-game and the Gp-game, defined for each p ∈ ω∗. We prove that for each p ∈ ω∗, there exists a space in which none of the players of the Gp-game has a winning strategy.Nevertheless a result of P. Nyikos, essentially shows that it is consistent, that there exists a countable space in which all these games are undetermined.We construct a countably compact space in which player II of the Gp-game is the winner, for every p ∈ ω∗. With the same technique of construction we built a countably compact space X, such that in X ×X player II of the G-game is the winner. Our last result is to construct ω1-many countably compact spaces, with player I of the G-game as a winner in any countable product of them, but player II is the winner in the product of all of them in the G-game.
2017-09-07T11:44:11Z∆-normal spaces and decompositions of normalityDas, A.K.https://riunet.upv.es:443/handle/10251/867012019-12-02T22:04:13Z2017-09-07T11:40:31Z∆-normal spaces and decompositions of normality
Das, A.K.
[EN] Generalizations of normality, called (weakly) (functionally) ∆-normal spaces are introduced and their interrelation with some existing notions of normality is studied. ∆-regular spaces are introduced which is a generalization of seminormal, semiregular and θ-regular space. This leads to decompositions of normality in terms of ∆-regularity, seminormality and variants of ∆-normality
2017-09-07T11:40:31ZContinuous utility functions on submetrizable hemicompact k-spacesCaterino, AlessandroCeppitelli, RitaMaccarino, Francescahttps://riunet.upv.es:443/handle/10251/867002019-12-02T22:04:13Z2017-09-07T11:36:58ZContinuous utility functions on submetrizable hemicompact k-spaces
Caterino, Alessandro; Ceppitelli, Rita; Maccarino, Francesca
[EN] Some theorems concerning the existence of continuous utility functions for closed preorders on submetrizable hemicompact k-spaces are proved. These spaces are precisely the inductive limits of increasing sequences of metric compact subspaces and in general are neither metrizable nor locally compact. These results generalize some well known theorems due to Levin.
2017-09-07T11:36:58ZConvergence semigroup actions: generalized quotientsBoustique, H.Mikusinski, PiotrRichardson, Garyhttps://riunet.upv.es:443/handle/10251/866982019-12-02T22:04:13Z2017-09-07T11:33:08ZConvergence semigroup actions: generalized quotients
Boustique, H.; Mikusinski, Piotr; Richardson, Gary
[EN] Continuous actions of a convergence semigroup are investigated in the category of convergence spaces. Invariance properties of actions as well as properties of a generalized quotient space are presented
2017-09-07T11:33:08Z