Skip to main content Accessibility help
×
Home

A note on the theorem of Baturov

  • María Muñoz (a1)

Extract

D.P. Baturov proved in ‘Subspaces of function spaces’ Vestnik Moskov University Series I (1987) that Lindelöf degree equals extent for subspaces of Cp(Χ) when Χ is a Lindelöf Σ-space. We prove that if the Lindelöf degree of the subspace is “big enough” the equality is true for a topological space Χ not necessarily Lindelöf Σ.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A note on the theorem of Baturov
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      A note on the theorem of Baturov
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      A note on the theorem of Baturov
      Available formats
      ×

Copyright

References

Hide All
[1]Arkhangel'skiĭ, A.V., ‘On some topological spaces that arise in functional analysis’, Russian Math. Surveys 31 (1976), 1430.
[2]Arkhangel'skiĭ, A.V., Topological function spaces, Mathematics and its Applications (Soviet Series) 78 (Kluwer Academic Publishers Group, Dordrecht, 1989). Translated from the Russian by Hoksbergen, R.A.M..
[3]Arkhangel'skiĭ, A.V. and Buzyakova, R., ‘Addition theorems and D-spaces’, Comment. Math. Univ. Car. 43 (2002), 653663.
[4]Arkhangel'skiĭ, A.V., ‘D-spaces and finite unions’, Proc. Amer. Math. Soc. 132 (2004), 21632170.
[5]Baturov, D.P., ‘Subspaces of function spaces’, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 4 (1987), 6669.
[6]Borges, C.R. and Wehrly, A.C., ‘A study on D-spaces’, Topology Proc. 16 (1991), 715.
[7]Cascales, B. and Oncina, L., ‘Compactoid filters and USCO maps’, J. Math. Anal. Appl. 282 (2003), 826845.
[8]Buzyakova, R., ‘Hereditarily D-property of function spaces over compacta’, Proc. Amer. Math. Soc. 132 (2004), 34333439.
[9]Cascales, B., Muñoz, M., and Orihuela, J., ‘Index of K-determination of topological spaces’, (preprint).
[10]van Douwen, E.K. and Pfeffer, W., ‘Some properties of the Sorgenfrey line and related spaces’, Pacific J. Math. 81 (1979), 371377.
[11]Engelking, R., General topology (PWN-Polish Scientific Publishers, Warsaw, 1977). Translated from the Polish by the author, Matematyczne, Monografie, Tom 60. [Mathematical Monographs, Vol. 60].
[12]Fleissner, W. and Stanley, A., ‘D-spaces’, Topology Appl. 114 (2001), 261271.
[13]Gruenhage, G., ‘A note on D-spaces’, Topology Appl. 153 (2006), 22292240.
[14]Hödel, R., ‘On a Theorem of Arkhangel'skiĭ concerning Lindelöf p-spaces’, Canad. J. Math. 27 (1975), 459468.
[15]Hödel, R., ‘Cardinal Functions I’, in Handbook of Set-Theoretic Topology (Elsevier Science Publishers, 1984), pp. 161.
[16]Kelley, J.L., General topology (Springer-Verlag, New York, 1975). Reprint of the 1955 edition [Van Nostrand, Toronto, Ont.], Graduate Texts in Mathematics 27.
[17]Nagami, K., ‘Σ-spaces’, Fund. Math. 65 (1969), 169192.
[18]Rogers, A. and Jayne, E., Analytic sets (Academic Press, London, 1980).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

A note on the theorem of Baturov

  • María Muñoz (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed