DSpace Collection: Volume 24 Number 1
http://hdl.handle.net/10525/515
Serdica Mathematical Journal Volume 24, Number 1, 1998The Collection's search engineSearch the Channelsearch
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Pseudoradial Spaces: Finite Products and an Example From CH
http://hdl.handle.net/10525/551
Title: Pseudoradial Spaces: Finite Products and an Example From CH<br/><br/>Authors: Simon, Petr; Tironi, Gino<br/><br/>Abstract: Aiming to solve some open problems concerning pseudoradialspaces, we shall present the following: Assuming CH, there are two semiradial spaces without semi-radial product. A new property of pseudoradialspaces insuring the pseudoradiality of a product is presented.<br/><br/>Description: ∗ The first named author’s research was partially supported by GAUK grant no. 350,partially by the Italian CNR. Both supports are gratefully acknowledged. The second authorwas supported by funds of Italian Ministery of University and by funds of the University ofTrieste (40% and 60%).Regular and Other Kinds of Extensions of Topological Spaces
http://hdl.handle.net/10525/550
Title: Regular and Other Kinds of Extensions of Topological Spaces<br/><br/>Authors: Dimov, G.<br/><br/>Abstract: In this paper the notion of SR-proximity is introduced and invirtue of it some new proximity-type descriptions of the ordered sets of all(up to equivalence) regular, resp. completely regular, resp. locally compactextensions of a topological space are obtained. New proofs of the SmirnovCompactification Theorem [31] and of the Harris Theorem on regular-closedextensions [17, Thm. H] are given. It is shown that the notion of SR-proximity is a generalization of the notions of RC-proximity [17] and Efremovicˇ proximity [15]. Moreover, there is a natural way for coming to both these notions starting from the SR-proximities. A characterization (in thespirit of M. Lodato [23, 24]) of the proximity relations induced by the regular extensions is given. It is proved that the injectively ordered set of all(up to equivalence) regular extensions of X in which X is 2-combinatoriallyembedded has a largest element (κX, κ). A construction of κX is proposed.A new class of regular spaces, called CE-regular spaces, is introduced; theclass of all OCE-regular spaces of J. Porter and C. Votaw [29] (and, hence,the class of all regular-closed spaces) is its proper subclass. The CE-regularextensions of the regular spaces are studied. It is shown that SR-proximitiescan be interpreted as bases (or generators) of the subtopological regularnearness spaces of H. Bentley and H. Herrlich [4].<br/><br/>Description: ∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.A Note on Totally Bounded Quasi-Uniformities
http://hdl.handle.net/10525/549
Title: A Note on Totally Bounded Quasi-Uniformities<br/><br/>Authors: Fletcher, P.; Hunsaker, W.<br/><br/>Abstract: We present the original proof, based on the Doitchinov completion, that a totally bounded quiet quasi-uniformity is a uniformity. Theproof was obtained about ten years ago, but never published. In the mean-time several stronger results have been obtained by more direct arguments[8, 9, 10]. In particular it follows from Künzi’s [8] proofs that each totallybounded locally quiet quasi-uniform space is uniform, and recently Déak[10] observed that even each totally bounded Cauchy quasi-uniformity is auniformity.P-Sequential Spaces and Cleavability
http://hdl.handle.net/10525/548
Title: P-Sequential Spaces and Cleavability<br/><br/>Authors: Koinac, Ljubia<br/><br/>Abstract: We consider some relations between p-sequential-like propertiesand cleavability of topological spaces. Under a special assumption we givean very easy proof of the following result of A.V. Arhangel’skii (the mainresult in [1]): if a (countably) compact space X is cleavable over the classof sequential spaces, then X is also sequential.<br/><br/>Description: ∗ Supported by the Serbian Scientific Foundation, grant No 04M01The Doitchinov Completion of a Regular Paratopological Group
http://hdl.handle.net/10525/547
Title: The Doitchinov Completion of a Regular Paratopological Group<br/><br/>Authors: Künzi, Hans-Peter; Romaguera, Salvador; Sipacheva, Ol’ga<br/><br/>Abstract: We show that the two-sided quasi-uniformity UB of a regularparatopological group (G, ·) is quiet. The Doitchinov completion (G, UB )of (G, UB ) can be considered a paratopological group containing G as adoubly dense subgroup whenever G is Abelian. Furthermore UB is the two-sided quasi-uniformity of (G, ·). These results generalize in an appropriateway important results about topological groups to regular paratopologicalgroups. A counterexample dealing with the non-Abelian case is presented.Furthermore we give conditions, depending on quasi-uniform completenessproperties, under which a paratopological group is a topological group.<br/><br/>Description: In memory of Professor D. Doitchinov∗ This paper was written while the first author was supported by the Swiss National Science Foundation under grants 21–30585.91 and 2000-041745.94/1 and by the Spanish Ministry ofEducation and Sciences under DGES grant SAB94-0120. The second author was supportedunder DGES grant PB95-0737. During her stay at the University of Berne the third authorwas supported by the first author’s grant 2000-041745.94/1 from the Swiss National ScienceFoundation.Dense Continuity and Selections of Set-Valued Mappings
http://hdl.handle.net/10525/546
Title: Dense Continuity and Selections of Set-Valued Mappings<br/><br/>Authors: Kenderov, Petar; Moors, Warren; Revalski, Julian<br/><br/>Abstract: A theorem proved by Fort in 1951 says that an upper or lowersemi-continuous set-valued mapping from a Baire space A into non-emptycompact subsets of a metric space is both lower and upper semi-continuousat the points of a dense Gδ -subset of A. In this paper we show that the conclusion of Fort’s theorem holds under the weaker hypothesis of either upper or lower quasi-continuity. Theexistence of densely defined continuous selections for lower quasi-continuousmappings is also proved.<br/><br/>Description: ∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.Projectively Solid Sets and an N-dimensional Piccard's Theorem
http://hdl.handle.net/10525/545
Title: Projectively Solid Sets and an N-dimensional Piccard's Theorem<br/><br/>Authors: Lindgren, W.; Szymanski, A.<br/><br/>Abstract: We discuss functions f : X × Y → Z such that sets of the formf (A × B) have non-empty interiors provided that A and B are non-emptysets of second category and have the Baire property.Co-Connected Spaces
http://hdl.handle.net/10525/544
Title: Co-Connected Spaces<br/><br/>Authors: Trnková, Vera<br/><br/>Abstract: Co-connected spaces, i.e. the spaces X for which any continuous mapX^2 → X factors through a projection, are investigated. The mainresult: every free monoid is isomorphic to the monoid of all nonconstantcontinuous selfmaps of a metrizable co-connected space.<br/><br/>Description: ∗ Financial support of the Grant Agency of the Czech Republic under the grant no 201/96/0119 and of the Grant Agency of the Charles University under the grant GAUK 149 isgratefully acknowledged.Doitchinov's Construct of Supertopological Spaces is Topological
http://hdl.handle.net/10525/543
Title: Doitchinov's Construct of Supertopological Spaces is Topological<br/><br/>Authors: Bentley, H.; Herrlich, Horst<br/><br/>Abstract: It is shown that the construct of supertopological spaces and continuous maps is topological.Isomorphism Problems for the Baire Function Spaces of Topological Spaces
http://hdl.handle.net/10525/542
Title: Isomorphism Problems for the Baire Function Spaces of Topological Spaces<br/><br/>Authors: Choban, Mitrofan<br/><br/>Abstract: Let a compact Hausdorff space X contain a non-empty perfectsubset. If α < β and β is a countable ordinal, then the Banach spaceBα (X) of all bounded real-valued functions of Baire class α on X is a propersubspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topologygenerated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number,then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and inthe case when X contains an uncountable compact metrizable space – byF.K.Dashiell [9]. Our argumentation is one non-metrizable modification ofboth Bade’s and Dashiell’s methods.On a Class of D-Cauchy Filters
http://hdl.handle.net/10525/541
Title: On a Class of D-Cauchy Filters<br/><br/>Authors: Császár, Ákos<br/><br/>Abstract: In a quasi-uniform space, firmly D-Cauchy filters are introduced and they role in constructing firm extensions is investigated.<br/><br/>Description: ∗ Research supported by Hungarian National Foundation for Scientific Research, Grant No T 016094.Doitchin Doitchinov - Biographical data
http://hdl.handle.net/10525/540
Title: Doitchin Doitchinov - Biographical data<br/><br/>Authors: Doitchinov, Doitchin<br/><br/>Abstract: Doitchin Doitchinov - Biographical data (pp. iv-v), List of publications (pp. vi-viii)