# I-weight, special base properties and related covering properties

Metadata Field | Value | Language |
---|---|---|

dc.contributor.advisor | Gruenhage, Gary | |

dc.contributor.advisor | Zenor, Phillip | en_US |

dc.contributor.advisor | Baldwin, Stewart | en_US |

dc.contributor.advisor | Shen, Wenxian | en_US |

dc.contributor.author | Bailey, Bradley | en_US |

dc.date.accessioned | 2008-09-09T21:18:54Z | |

dc.date.available | 2008-09-09T21:18:54Z | |

dc.date.issued | 2005-12-15 | en_US |

dc.identifier.uri | http://hdl.handle.net/10415/504 | |

dc.description.abstract | Alleche, Arhangel'ski\u{\i} and Calbrix defined the notion of a sharp base and posed the question: Is there a regular space with a sharp base whose product with [0, 1] does not have a sharp base? Chapter 2 contains an example of a space $P$ with a sharp base whose product with [0, 1] does not have a sharp base. The example in Chapter 2 also answers the following 3 questions found in the literature: Is every pseudocompact Tychonoff space with a sharp base metrizable? Is there a pseudocompact space $X$ with a G$_\delta$-diagonal and a point-countable base such that $X$ is not developable? Is every \v{C}ech-complete pseudocompact space with a point-countable base metrizable? The space we construct is pseudocompact, \v{C}ech-complete, has a G$_\delta$-diagonal, a sharp base and a point-countable base, but is not metrizable nor developable. In Chapter 3, we study open-in-finite (OIF) bases and introduce the notion of a $\delta$-open-in-finite ($\delta$-OIF) base. Each $\delta$-OIF base is also OIF. We show that a base $\mathcal{B}$ for the space $X$ is $\delta$-OIF if and only if for each dense subset $Y$ of $X$, $\mathcal{B} \upharpoonright Y$ is OIF. We also define OIF-metacompact, $\delta$-OIF-metacompact, $(n, \kappa)$-metacompact, and $(<\omega, \kappa)$-metacompact and show that for generalized order spaces and $\kappa = \omega$ these properties are equivalent. The $(<\omega, \omega)$-metacompact property is corresponds to the $< \omega$-weakly uniform base property. We show that for Moore spaces $X$, the space $X$ has an OIF base (resp. $\delta$-OIF base, $<\omega$-weakly uniform base) if and only if the space is OIF-metacompact (resp. $\delta$-OIF-metacompact, $(<\omega, \omega)$-metacompact). In the final chapter, we prove that for the class of linearly ordered compact spaces, i-weight reflects all cardinals. We find necessary and sufficient conditions for i-weight to reflect cardinal $\kappa$ in the class of locally compact linearly ordered spaces. In the last section we calculate the i-weight of paracompact spaces in terms of the local i-weight and extent of the space. This result determines that for compact spaces i-weight and local i-weight are the same. | en_US |

dc.language.iso | en_US | en_US |

dc.subject | Mathematics and Statistics | en_US |

dc.title | I-weight, special base properties and related covering properties | en_US |

dc.type | Dissertation | en_US |

dc.embargo.length | NO_RESTRICTION | en_US |

dc.embargo.status | NOT_EMBARGOED | en_US |