Intrinsic characterizations of C-realcompact spaces

• Acharyya, Sudip Kumar ^[1] ; Bharati, Rakesh ^[1] ; Deb Ray, Atasi ^[1]
  1. [1] University of Calcutta

     University of Calcutta

     India

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 2, 2021, págs. 295-302
• Idioma: inglés
• DOI: 10.4995/agt.2021.13696
• Enlaces
  • Texto completo
• Resumen

  • c-realcompact spaces are introduced by Karamzadeh and Keshtkar in Quaest. Math. 41, no. 8 (2018), 1135-1167. We offer a characterization of these spaces X via c-stable family of closed sets in X by showing that  X is c-realcompact if and only if each c-stable family of closed sets in X with finite intersection property has nonempty intersection. This last condition which makes sense for an arbitrary topological space can be taken as an alternative definition of a c-realcompact space. We show that each topological space can be extended as a dense subspace to a c-realcompact space with some desired extension properties. An allied class of spaces viz CP-compact spaces akin to that of c-realcompact spaces are introduced. The paper ends after examining how far a known class of c-realcompact spaces could be realized as CP-compact for appropriately chosen ideal P of closed sets in X.

• Referencias bibliográficas
  • S. K. Acharyya and S. K. Ghosh, A note on functions in C(X) with support lying on an ideal of closed subsets of X, Topology Proc. 40 (2012),...
  • S. K. Acharyya and S. K. Ghosh, Functions in C(X) with support lying on a class of subsets of X, Topology Proc. 35 (2010), 127-148.
  • S. K. Acharyya, R. Bharati and A. Deb Ray, Rings and subrings of continuous functions with countable range, Queast. Math., to appear. https://doi.org/10.2989/16073606.2020.1752322
  • F. Azarpanah, O. A. S. Karamzadeh, Z. Keshtkar and A. R. Olfati, On maximal ideals of $C_c(X)$ and the uniformity of its localizations, Rocky...
  • P. Bhattacherjee, M. L. Knox and W. W. Mcgovern, The classical ring of quotients of $C_c(X)$, Appl. Gen. Topol. 15, no. 2 (2014), 147-154....
  • L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand Reinhold co., New York, 1960. https://doi.org/10.1007/978-1-4615-7819-2
  • M. Ghadermazi, O. A. S. Karamzadeh and M. Namdari, On the functionally countable subalgebras of C(X), Rend. Sem. Mat. Univ. Padova. 129 (2013),...
  • O. A. S. Karamzadeh and Z. Keshtkar, On c-realcompact spaces, Queast. Math. 41, no. 8 (2018), 1135-1167. https://doi.org/10.2989/16073606.2018.1441919
  • M. Mandelkar, Supports of continuous functions, Trans. Amer. Math. Soc. 156 (1971), 73-83. https://doi.org/10.1090/S0002-9947-1971-0275367-4
  • R. M. Stephenson Jr, Initially k-compact and related spaces, in: Handbook of Set-Theoretic Topology, ed. Kenneth Kunen and Jerry E. Vaughan....
  • A. Veisi, $e_c$-filters and $e_c$-ideals in the functionally countable subalgebra of $C^*(X)$, Appl. Gen. Topol. 20, no. 2 (2019), 395-405....