Document Details

Document Type : Thesis 
Document Title :
On Joint Metrizability of Spaces and ω-continuous Mappings
عن قابلية القياس بشكل مشترك للفراغات ودوال أوميقا المتصلة
 
Subject : Faculty of Science 
Document Language : Arabic 
Abstract : Given a topological space X, we say that X is separably metrizable if X is jointly metrizable on the family of all separable subspaces of X. We present some elementary properties of separably metrizable spaces. We show that separably metrizable spaces are equivalent to countably metrizable spaces. Also, we show that for ω-bounded spaces, separably metrizable spaces are equivalent to compactly metrizable spaces. We present a metrization theorem for union of spaces, a topological space X which is the union of open metrizable subspaces is metrizable if and only if X is separably metrizable (Theorem 3.3.5). We study also joint metrizability on finite subspaces and we prove that the class of T1-spaces is equivalent to the class of finitely metrizable spaces. In addition, joint metrizability on first countable subspaces and Lindelöf subspaces are investigated. Furthermore, we study ω-leaders of topological spaces, ω-continuous mappings and ω-spaces. We obtain some new properties of these structures. Among them, we show that the ω-leader of a T1 P-space is a discrete space. We also prove that a topological space is separable if and only if its ω-leader is separable. It is shown that ω-continuous mappings preserve the class of separable spaces and the class of sequentially compact spaces. 
Supervisor : Dr. Mohammed Ahmed Al Shumrani 
Thesis Type : Master Thesis 
Publishing Year : 1441 AH
2020 AD 
Added Date : Tuesday, June 9, 2020 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
أحمد محمد صهلوليSahloli, Ahmad MohammedResearcherMaster 

Files

File NameTypeDescription
 46344.pdf pdf 

Back To Researches Page