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1.
Samuel G. da Silva 《Acta Mathematica Hungarica》2014,142(2):420-432
We investigate a selective version of property (a) and prove a number of results showing that, under certain set theoretical conditions, (a) spaces and selectively (a) spaces behave in a very similar way, at least for separable spaces. Several results regarding the presence of the referred selective version in spaces from almost disjoint families are established; in particular, we give a combinatorial characterization of such presence. Consistent set theoretical hypotheses implying equivalence between being (a) and being selectively (a) within the referred class are presented, as well as hypotheses implying non-equivalence. We also show that the Continuum Hypothesis is independent of the statement asserting the above mentioned equivalence. The paper finishes by presenting some notes and questions on the role of set theoretical assumptions in the subject. 相似文献
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(LF)-空间的完备性 总被引:1,自引:0,他引:1
设(E,ξ)=indlim(E.,ξn)为Frechel空间序列的诱导权限,我们证明了:若每个(Enξ|En)正速完备,则(E,ξ)=indlim(En,ξn)为完备,进而证明了;若对于每个自然数n,存在自然数m(n)使对于任意p≥m(n)有En;则(E,ξ)为完备. 相似文献
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Carmen Fernández 《Archiv der Mathematik》1990,54(4):380-383
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D. van Dulst 《Mathematische Annalen》1976,224(2):111-115
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Jerzy Kakol 《Rendiconti del Circolo Matematico di Palermo》1993,42(3):453-458
Developing ideas found in a recent paper of Gilsdorf to arbitrary topological vector spaces (tvs) one shows that a Hausdorff (LB)
tv
-spaceE is regular provided every null-sequence inE has a series convergent subsequence inE.
Received by the editors 1980Mathematics Subject Classification (1985 Revision) 46A12. 相似文献
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J. M. García-Lafuente 《Monatshefte für Mathematik》1987,103(2):115-120
Once the existence of metrizable (LF)-spaces was discovered, the problem whether the completion of an (LF)-space is or is not an (LF)-space was answered in the negative, because no (LF)-space can be a Fréchet space. However, some (non-metrizable) (LF)-spaces are complete, e.g. the classical Köthe's strict (LF)-spaces. In this paper we will carry out a thorough study of the completeness of (LF)-spaces stressing upon the stable completion properties of (LB)-spaces. A basic tool for handling this problem is an Open Mapping Theorem for completions of (LF)-spaces, which is also proved in the present paper.This research, supported by a Fulbright-MEC fellowship, was carried out during the author's visit at the University of Maryland while on leave from the University of Extremadura. The author is grateful to Professor S. A. Saxon for very helpful conversation and, especially, for calling his attention to the problem of completions of (LF)-spaces. 相似文献
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F. A. Sukochev 《Mathematical Notes》1992,52(6):1280-1282
Translated from Matematicheskie Zametki, Vol. 52, No. 6, pp. 149–151, December, 1992. 相似文献
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Jochen Wengenroth 《Results in Mathematics》1997,32(1-2):169-178
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Volker Wrobel 《Mathematische Zeitschrift》1980,174(3):281-287
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王树泉 《纯粹数学与应用数学》2002,18(4):357-361
通过在S(3)-空间中引入概念θ^2-绝对,建立了S(2)-闭的S(3)-空间与紧空间的联系,并且给出了几个与之相关的性质。 相似文献
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A representation of the CD 0(K)-space is given in [1, 2] for a compact Hausdorff space K without isolated points. We generalize this to an arbitrary countably compact space K without any assumption on isolated points. 相似文献
18.
Let U be an absolutely convex open subset of a complex barrelled (DF)-space E and let F be a commutative Banach algebra with identity. Let Hb(U, F) be the space of holomorphic mappings from U into F that are bounded on the U-bounded sets and let Hb (U, F) be the space of the holomorphic mappings from U into F that are uniformly weakly continuous on the U-bounded sets, both endowed with the topology τb of uniform convergence on the U-bounded sets. The spectra of (Hwu (U, F), τb) and (Hb(U, F), τb) are studied. 相似文献
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