# NEW CARDINAL FUNCTIONS RELATED TO ALMOST CLOSED SETS

Cho, Myung Hyun;Moon, Mi Ae;Kim, Junhui

• Accepted : 2013.08.15
• Published : 2013.09.25
• 29 1

#### 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

almost closed;${\kappa}$-AP;${\kappa}$-WAP;${\kappa}$-radial;${\kappa}$-pseudoradial

#### References

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#### 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

#### Acknowledgement

Supported by : Wonkwang University