Π -Normality In Topological Spaces And Its Generalization
The main aim of this thesis is to make a comprehensive study of a weaker version of normality called p-normality, which lies between normality and almost normality (quasi-normality). First, we give some basic definitions, properties and theorems, which we are going to use throughout the thesis. We g...
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my-usm-ep.462072020-02-13T07:06:23Z Π -Normality In Topological Spaces And Its Generalization 2013-11 Thabit, Sadeq Ali Saad QA1 Mathematics (General) The main aim of this thesis is to make a comprehensive study of a weaker version of normality called p-normality, which lies between normality and almost normality (quasi-normality). First, we give some basic definitions, properties and theorems, which we are going to use throughout the thesis. We give a survey study of Π-closed, p-open, pre-closed and pre-open sets. In particular, we study these sets in subspaces and also study the images and the inverse images of them under continuous functions. Some properties of these sets are given and proved. Π-normality is both a topological and an additive property, but neither a productive nor a hereditary property in general. The notion of Π-generalized closed sets is used to obtain various characterizations and preservation theorems of Π-normality. Some properties of almost regular as well as almost completely regular spaces are presented, and a few results of them are improved. Some relationships between Π-normality and both almost regularity and almost complete regularity are given. The important results are about presenting some counterexamples, the first one is about a semi-normal Hausdorff space but not Π-normal. The second one is about an almost normal Tychonoff space but not quasi-normal and the third one is about an almost normal Tychonoff space but not Π-normal. 2013-11 Thesis http://eprints.usm.my/46207/ http://eprints.usm.my/46207/1/Sadeq%20Ali%20Saad%20Thabit24.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik |
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Universiti Sains Malaysia |
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USM Institutional Repository |
| language |
English |
| topic |
QA1 Mathematics (General) |
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QA1 Mathematics (General) Thabit, Sadeq Ali Saad Π -Normality In Topological Spaces And Its Generalization |
| description |
The main aim of this thesis is to make a comprehensive study of a weaker version of normality called p-normality, which lies between normality and almost normality (quasi-normality). First, we give some basic definitions, properties and theorems, which we are going to use throughout the thesis. We give a survey study of Π-closed, p-open, pre-closed and pre-open sets. In particular, we study these sets in subspaces and also study the images and the inverse images of them under continuous functions. Some properties of these sets are given and proved. Π-normality is both a topological and an additive property, but neither a productive nor a hereditary property in general. The notion of Π-generalized closed sets is used to obtain various characterizations and preservation theorems of Π-normality. Some properties of almost regular as well as almost completely regular spaces are presented, and a few results of them are improved. Some relationships between Π-normality and both almost regularity and almost complete regularity are given. The important results are about presenting some counterexamples, the first one is about a semi-normal Hausdorff space but not Π-normal. The second one is about an almost normal Tychonoff space but not quasi-normal and the third one is about an almost normal Tychonoff space but not Π-normal. |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Thabit, Sadeq Ali Saad |
| author_facet |
Thabit, Sadeq Ali Saad |
| author_sort |
Thabit, Sadeq Ali Saad |
| title |
Π -Normality In Topological Spaces And Its Generalization |
| title_short |
Π -Normality In Topological Spaces And Its Generalization |
| title_full |
Π -Normality In Topological Spaces And Its Generalization |
| title_fullStr |
Π -Normality In Topological Spaces And Its Generalization |
| title_full_unstemmed |
Π -Normality In Topological Spaces And Its Generalization |
| title_sort |
π -normality in topological spaces and its generalization |
| granting_institution |
Universiti Sains Malaysia |
| granting_department |
Pusat Pengajian Sains Matematik |
| publishDate |
2013 |
| url |
http://eprints.usm.my/46207/1/Sadeq%20Ali%20Saad%20Thabit24.pdf |
| _version_ |
1747821632128286720 |