Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A STUDY ON κ-AP, κ-WAP SPACES AND THEIR RELATED SPACES

  • Cho, Myung Hyun (Department of Mathematics Education Wonkwang University) ;
  • Kim, Junhui (Department of Mathematics Education Wonkwang University)
  • Received : 2017.10.17
  • Accepted : 2017.11.24
  • Published : 2017.12.25
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Abstract

In this paper we define $AP_c$ and $AP_{cc}$ spaces which are stronger than the property of approximation by points(AP). We investigate operations on their subspaces and study function theorems on $AP_c$ and $AP_{cc}$ spaces. Using those results, we prove that every continuous image of a countably compact Hausdorff space with AP is AP. Finally, we prove a theorem that every compact ${\kappa}$-WAP space is ${\kappa}$-pseudoradial, and prove a theorem that the product of a compact ${\kappa}$-radial space and a compact ${\kappa}$-WAP space is a ${\kappa}$-WAP space.

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References

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