Title: | Factorizations of normality via generalizations of $\beta $-normality (English) |

Author: | Das, Ananga Kumar |

Author: | Bhat, Pratibha |

Author: | Gupta, Ria |

Language: | English |

Journal: | Mathematica Bohemica |

ISSN: | 0862-7959 (print) |

ISSN: | 2464-7136 (online) |

Volume: | 141 |

Issue: | 4 |

Year: | 2016 |

Pages: | 463-473 |

Summary lang: | English |

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Category: | math |

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Summary: | The notion of $\beta $-normality was introduced and studied by Arhangel'skii, Ludwig in 2001. Recently, almost $\beta $-normal spaces, which is a simultaneous generalization of $\beta $-normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak $\beta $-normality, in terms of $\theta $-closed sets, which turns out to be a simultaneous generalization of $\beta $-normality and $\theta $-normality. A space $X$ is said to be weakly $\beta $-normal (w$\beta $-normal$)$ if for every pair of disjoint closed sets $A$ and $B$ out of which, one is $\theta $-closed, there exist open sets $U$ and $V$ such that $\overline {A\cap U}=A$, $\overline {B\cap V}=B$ and $\overline {U}\cap \overline {V}=\emptyset $. It is shown that w$\beta $-normality acts as a tool to provide factorizations of normality. (English) |

Keyword: | normal space |

Keyword: | (weakly) densely normal space |

Keyword: | (weakly) $\theta $-normal space |

Keyword: | almost normal space |

Keyword: | almost $\beta $-normal space |

Keyword: | $\kappa $-normal space |

Keyword: | (weakly) $\beta $-normal space |

MSC: | 54D15 |

idZBL: | Zbl 06674856 |

idMR: | MR3576793 |

DOI: | 10.21136/MB.2016.0048-15 |

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Date available: | 2017-01-03T15:15:00Z |

Last updated: | 2020-07-01 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/145953 |

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