Document Details

Document Type : Thesis 
Document Title :
EPI-MILDLY NORMAL AND PARTIALLY NORMAL TOPOLOGICAL SPACES
الفراغات التبولوجية إبي- الناظمة المعتدلة و الناظمة الجزئية
 
Subject : Faculty of Science 
Document Language : Arabic 
Abstract : This dissertation is a comprehensive study of two new topological proporties. The first one is epi-mild normality and the second one is partial normality. \bigskip A space ($X$ ,{\Large$\tau$} ) is epi-mildly normal if there is a coarser topology {\Large$\tau$}$^\prime$ on $X$ such that ($X$ , {\Large$\tau$}$^\prime$ ) is Hausdorff mildly normal. It lies between submetrizability and epinormality, but it is independent from them. It is an additive topological property but not multiplicative in general. We present conditions about multiplicity. We establish other properties of epi-mild normality. \bigskip A space $X$ is partially normal if for any two disjoint subsets $A$ and $B$ of $X$, where $A$ is closed domain and $B$ is $\pi$-closed, there exist two disjoint open subsets $U$ and $V$ of $X$ such that $A\subseteq U$ and $B\subseteq V$. It lies between almost normality and mild normality and between quasi-normality and mild normality, but it is independent from all of them. It is an additive topological property but not multiplicative. We present a Mr\{o}wka space which is not partailly normal and use the continuum hypothesis (CH) to build another Mr\{o}wka space which is partailly normal. We also establish other properties of partial normality. 
Supervisor : Dr. Lutfi Kalantan 
Thesis Type : Doctorate Thesis 
Publishing Year : 1440 AH
2018 AD 
Added Date : Sunday, November 11, 2018 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
ابتسام عيد الشمريAlshammari, Ibtesam EidResearcherDoctorate 

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