Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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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
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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.

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References

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