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A NOTE ON SPACES Cp(X)K-ANALYTIC-FRAMED IN ℝX

  • J. C. FERRANDO (a1) and J. KĄKOL (a2)
Abstract
Abstract

This paper characterizes the K-analyticity-framedness in ℝX for Cp(X) (the space of real-valued continuous functions on X with pointwise topology) in terms of Cp(X). This is used to extend Tkachuk’s result about the K-analyticity of spaces Cp(X) and to supplement the Arkhangel skiĭ–Calbrix characterization of σ-compact cosmic spaces. A partial answer to an Arkhangel skiĭ–Calbrix problem is also provided.

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Copyright
Corresponding author
For correspondence; e-mail: jc.ferrando@umh.es
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The research of both authors has been supported by project MTM2005-01182 of the Spanish Ministry of Education and Science, co-financed by the European Community (Feder funds). The second named author was also supported by grant MNiSW Nr. N N201 2740 33 as well as by the Technical University of Valencia (September 2007) with the grant ‘Ayuda para estancias de investigadores de prestigio en la UPV’.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] A. V. Arkhangel′skiĭ , Topological Function Spaces, Math. and its Applications, 78 (Kluwer Academic Publishers, Dordrecht, 1992).

[3] A. V. Arkhangel′skiĭ , ‘Function spaces in the topology of pointwise convergence and compact sets’, Russian Math. Surveys 39 (1984), 956.

[4] A. V. Arkhangel′skiĭ and J. Calbrix , ‘A characterization of σ-compactness of a cosmic space X by means of subspaces of ℝX’, Proc. Amer. Math. Soc. 127 (1999), 24972504.

[6] B. Cascales , ‘On K-analytic locally convex spaces’, Arch. Math. 49 (1987), 232244.

[7] B. Cascales and J. Orihuela , ‘On compactness in locally convex spaces’, Math. Z. 195 (1987), 365381.

[9] B. Cascales , J. Kąkol and S. A. Saxon , ‘Weight of precompact subsets and tightness’, J. Math. Anal. Appl. 269 (2002), 500518.

[10] B. Cascales , J. Kąkol and S. A. Saxon , ‘Metrizability vs. Fréchet–Urysohn property’, Proc. Amer. Math. Soc. 131 (2003), 36233631.

[14] J. C. Ferrando , ‘Two new properties of the space Cp(X)’, Topology Appl. 154 (2007), 17991803.

[15] J. C. Ferrando , J. Kąkol , M. López Pellicer and S. A. Saxon , ‘Quasi-Souslin weak duals’, J. Math. Anal. Appl. 339 (2008), 12531263.

[17] D. Lutzer , J. van Mill and R. Pol , ‘Descriptive complexity of function spaces’, Trans. Amer. Math. Soc. 291 (1985), 121128.

[18] O. G. Okunev , ‘On Lindelöf σ-spaces of continuous functions in the pointwise topology’, Topology Appl. 49 (1993), 149166.

[20] M. Talagrand , ‘Espaces de Banach faiblement K-analytiques’, Ann. of Math. 110 (1979), 407438.

[21] V. V. Tkachuk , ‘A space Cp(X) is dominated by irrationals if and only if it is K-analytic’, Acta Math. Hungar. 107(4) (2005), 253265.

[22] M. Valdivia , Topics in Locally Convex Spaces (North-Holland, Amsterdam, 1982).

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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