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NEW CARDINAL FUNCTIONS RELATED TO ALMOST CLOSED SETS

  • Cho, Myung Hyun (Department of Mathematics Education, Wonkwang University) ;
  • Moon, Mi Ae (Division of Mathematics & Informational Statistics, Wonkwang University) ;
  • Kim, Junhui (Department of Mathematics Education, Wonkwang University)
  • Received : 2013.07.31
  • Accepted : 2013.08.15
  • Published : 2013.09.25

Abstract

In this paper, we strengthen the properties of approximation by points (AP) and weak approximation by points (WAP) considered by A. Pultr and A. Tozzi in 1993 to define ${\kappa}$-AP and ${\kappa}$-WAP for an infinite cardinal ${\kappa}$. We also strengthen the properties of radial and pseudoradial to define ${\kappa}$-radial and ${\kappa}$-pseudoradial for an infinite cardinal ${\kappa}$. These allow us to consider new cardinal functions related to almost closed sets; AP-number, WAP-number, radial number, and pseudoradial number. We study their properties and show the relationships between them. We also provide some examples around ${\kappa}$-AP and ${\kappa}$-WAP which are closely connected with ${\kappa}$-radial and ${\kappa}$-pseudoradial.

Keywords

References

  1. A. V. Arhangel'skii, Bicompact sets and the topology of spaces, Soviet Mathematics, Doklady, 4 (1963), 561-564.
  2. A. Bella and I. V. Yaschenko, On AP and WAP spaces, Comment. Math. Univ. Carolin. 40(3) (1999), 531-536.
  3. R. Engelking, General Topology, Revised and completed edition, Heldermann Verlag, Berlin, 1989.
  4. W. C. Hong, Generalized Frechet-Urysohn Spaces, J. Korean Math. Soc. 44(2) (2007), 261-273. https://doi.org/10.4134/JKMS.2007.44.2.261
  5. A. Pultr and A. Tozzi, Equationally closed subframes and representation of quotient spaces, Cahiers Topologie Geom. Differentielle Categ. 34(3) (1993), 167-183.
  6. V. V. Tkachuk and I. V. Yaschenko, Almost closed sets and topologies they determine, Comment. Math. Univ. Carolin. 42(2) (2001), 393-403.

Cited by

  1. STRONG VERSIONS OF κ-FRÉCHET AND κ-NET SPACES vol.37, pp.4, 2015, https://doi.org/10.5831/HMJ.2015.37.4.549