• Title/Summary/Keyword: ${\kappa}$-pseudo-radial

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A STUDY ON κ-AP, κ-WAP SPACES AND THEIR RELATED SPACES

  • Cho, Myung Hyun;Kim, Junhui
    • Honam Mathematical Journal
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    • v.39 no.4
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    • pp.655-663
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    • 2017
  • 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.