NEW CARDINAL FUNCTIONS RELATED TO ALMOST CLOSED SETS

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 3,  2013, pp.541-550
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.3.541
Title & Authors
NEW CARDINAL FUNCTIONS RELATED TO ALMOST CLOSED SETS
Cho, Myung Hyun; Moon, Mi Ae; Kim, Junhui;

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 $\small{{\kappa}}$-AP and $\small{{\kappa}}$-WAP for an infinite cardinal $\small{{\kappa}}$. We also strengthen the properties of radial and pseudoradial to define $\small{{\kappa}}$-radial and $\small{{\kappa}}$-pseudoradial for an infinite cardinal $\small{{\kappa}}$. 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 $\small{{\kappa}}$-AP and $\small{{\kappa}}$-WAP which are closely connected with $\small{{\kappa}}$-radial and $\small{{\kappa}}$-pseudoradial.
Keywords
almost closed;$\small{{\kappa}}$-AP;$\small{{\kappa}}$-WAP;$\small{{\kappa}}$-radial;$\small{{\kappa}}$-pseudoradial;
Language
English
Cited by
1.
STRONG VERSIONS OF κ-FRÉCHET AND κ-NET SPACES,;;;

호남수학학술지, 2015. vol.37. 4, pp.549-557
1.
STRONG VERSIONS OF κ-FRÉCHET AND κ-NET SPACES, Honam Mathematical Journal, 2015, 37, 4, 549
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