|
Document Type |
: |
Thesis |
|
Document Title |
: |
Semi-regularization Topological Spaces الفراغات التوبولوجية المتناسقة جزيئياً |
|
Subject |
: |
Faculty of Science |
|
Document Language |
: |
Arabic |
|
Abstract |
: |
In this thesis, we introduce a standard way of constructing a new topological space from a given one. If (X‚τ) is a topological space, then the semi-regularization topology τ_(s )on X of τ is the coarser topology on X generated by the family of all open domains of (X‚τ) where a subset U is called an open domain if int(¯U)=U. Cameron has called a topological property P semi-regular provided that (X‚τ) has property P if and only if (X‚τ_(s ) ) has property P. This thesis is a continuation of the study that has been conducted by M. Mr\u{s}evi\'{c}, I. L. Reilly and M. K. Vamanamurthy in 1983 `` On semi-regular topological space ". τ_(s ) is called the semi-regularization topology on X induced by τ. (X‚τ_(s ) ) is called the semi-regularization topological space of (X‚τ). (X‚τ)is called semi-regular if and only if τ = τ_(s ), we always have τ_(s )⊆ τ . First, we study some of the fundamental properties between a topological space (X‚τ) and its semi-regularization space (X‚τ_(s ) ) such as compactness and some of its kind, separability and we give a detail study of the separation axioms. Then, we study the semi-regularity as a topological property for some generated spaces such as the Alexandroff duplicate, the closed extension, the open extension, and the discrete extension. Then, we extended our study to include some topological properties between a topological space (X‚τ) and its semi-regularization space (X‚τ_(s ) ) such as scattered, epi-normal, submetrizable, wD property, and C-normality. |
|
Supervisor |
: |
Prof. Lutfi Kalantan |
|
Thesis Type |
: |
Master Thesis |
|
Publishing Year |
: |
1444 AH
2022 AD |
|
Co-Supervisor |
: |
Dr. Dina Abuzaid |
|
Added Date |
: |
Monday, February 27, 2023 |
|
Researchers
| نوف حسن الفارسي | Alfarsi, Nouf Hassan | Researcher | Master | |
|