- Title
- On β-Normal Spaces
- Creator
- Ngcamphalala, Thobile
- ThesisAdvisor
- Nxumalo, Mbekezeli
- ThesisAdvisor
- Dube, Themba
- Subject
- Beta normal form
- Subject
- Open set
- Subject
- Bitopological space
- Subject
- Topology
- Date
- 2025-04-02
- Type
- Academic theses
- Type
- Master's theses
- Type
- text
- Identifier
- http://hdl.handle.net/10962/479186
- Identifier
- vital:78268
- Description
- This thesis revisits some types of normal spaces, namely, β-normal spaces and α-normal spaces, which were introduced by Arkhangel’skii and Ludwig in 2001. We study some properties of these spaces with a focus on improving some of the already existing properties and exploring new properties that are not available in the literature. Under β-normal spaces, among other things, we characterize these spaces using some types of open sets. We use the ultrafilter space to answer Murtinova’s question about the existence of a β-normal and regular space which is not Tychonoff. α-normal spaces are described in terms of countable open sets, a result imitating that of normality. It turns out that continuous functions which are onto, open and closed preserve β-normality, while those which are injective, open and closed reflect α-normality. The notion of β-normal spaces is extended to the category of bitopological spaces where we characterize these bitopological spaces simultaneously in terms of i-open sets, (i, j)-preopen and (i, j)-α-open sets. We study the interrelations of these spaces with other bitopological spaces.
- Description
- Thesis (MSc) -- Faculty of Science, Mathematics, 2025
- Format
- computer, online resource, application/pdf, 1 online resource (70 pages), pdf
- Publisher
- Rhodes University, Faculty of Science, Mathematics
- Language
- English
- Rights
- Ngcamphalala, Thobile
- Rights
- Use of this resource is governed by the terms and conditions of the Creative Commons "Attribution-NonCommercial-ShareAlike" License (http://creativecommons.org/licenses/by-nc-sa/2.0/)
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RU Department of Mathematics (Pure and Applied)
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details | SOURCE1 | NGCAMPHALALA-MSC-TR25-39.pdf | 816 KB | Adobe Acrobat PDF | View Details |