Rocky Mountain Journal of Mathematics

Some criteria for $C_p(X)$ to be an $L\Sigma(\le\o)$-space

V.V. Tkachuk

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 43, Number 1 (2013), 373-384.

First available in Project Euclid: 3 June 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54H11: Topological groups [See also 22A05] 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 22A05: Structure of general topological groups 54D06
Secondary: 54D25: "$P$-minimal" and "$P$-closed" spaces 54C25: Embedding

Lindelöf $\Sigma$-space $L\Sigma(\lt\omega)$-space $L\Sigma(\le\omega)$-space function space cosmic space network upper semicontinuous map


Tkachuk, V.V. Some criteria for $C_p(X)$ to be an $L\Sigma(\le\o)$-space. Rocky Mountain J. Math. 43 (2013), no. 1, 373--384. doi:10.1216/RMJ-2013-43-1-373.

Export citation


  • A.V. Arhangel'skii, Topological function spaces, Kluwer Academic Publishers, Dordrecht, 1992.
  • D.P. Baturov, On subspaces of function spaces, Vestnik MGU, Matematika, Mech. 42 (1987), 66-69 (in Russian).
  • R. Engelking, General topology, PWN, Warszawa, 1977.
  • R.E. Hodel, Cardinal functions I, in Handbook of set-theoretic topology, K. Kunen and J.E. Vaughan, eds., North Holland, Amsterdam, 1984.
  • W. Kubiś, O. Okunev and P.J. Szeptycki, On some classes of Lindelöf $\Sigma$-spaces, Topol. Appl. 153 (2006), 2574-2590.
  • I. Molina Lara and O. Okunev, $ L\Sigma(\le\o)$-spaces and spaces of continuous functions, Central European J. Math., to appear.
  • O.G. Okunev, Spaces of functions in the topology of pointwise convergence: Hewitt extension and $\tau$-continuous functions, Vestnik Mosk. Univ. Matem. 40 (1985), 84-87.
  • –––, On Lindelöf $\Sigma$-spaces of continuous functions in the pointwise topology, Topol. Appl. 49 (1993), 149-166.
  • –––, $L\Sigma(\kappa)$-spaces, in Open problems in topology, II, E. Pearl, ed., Elsevier, Amsterdam, 2007.
  • M.G. Tkačenko, ${\cal P}$-approximable compact spaces, Comment. Math. Univ. Carol. 32 (1991), 583-595.
  • V.V. Tkachuk, A glance at compact spaces which map “nicely" onto the metrizable ones, Topol. Proc. 19 (1994), 321-334.
  • –––, Behaviour of the Lindelöf $\Sigma$-property in iterated function spaces, Topol. Appl. 107 (2000), 297-305.
  • –––, Lindelöf $\Sigma$-property of $ C_p(X)$ together with countable spread of $ X$ implies $ X$ is cosmic, New Zealand J. Math. 30 (2001), 93-101.
  • –––, A space $ C_p(X)$ is dominated by irrationals if and only if it is $ K$-analytic, Acta Math. Hungar. 107 (2005), 261-273.
  • –––, Condensing function spaces into $\Sigma$-products of real lines, Houston J. Math. 33 (2007), 209-228. \noindentstyle