Advanced Topology-1 covers a variety of concepts and properties related to semi-open sets, mappings, continuity, and various types of topological spaces.

##### Let’s break down and explain each part:
1. Semi-Open Sets and Semi-Closed Sets:
• Semi-Open Sets: Sets that are both open and closed in some sense.
• Semi-Closed Sets: Sets that are both closed and not open. Elements in a semi-closed set may or may not be included in the boundary.
2. Semi-Open, Semi-Closed Mappings:
• Mappings that preserve semi-open or semi-closed sets under inverse image.
3. Almost Closed and Almost Open Mappings:
• Mappings that are nearly closed or nearly open, preserving certain properties.
4. s-Continuous, s-Open, and s-Closed Functions:
• s-Continuous Functions: Functions that preserve certain types of sets.
• s-Open and s-Closed Functions: Functions that behave analogously to semi-open and semi-closed sets.
5. Semi-Closure and Semi-Interior:
• Semi-Closure: An operation similar to closure but not necessarily capturing all limit points.
• Semi-Interior: Similar to interior but not necessarily capturing all interior points.
6. Weakly Continuous and Almost Continuous Mappings:
• Mappings that are nearly continuous or satisfy a weaker form of continuity.
7. Semi-Weekly Continuous Mappings and s-Connectedness:
• Mappings and spaces that exhibit a form of continuity and connectedness that is less stringent than traditional notions.
8. Strongly Continuous Mapping:
• Strongly Continuous Mapping: A more stringent form of continuity.
9. Semi-T Spaces, i=0,1,2 and Their Properties:
• Semi-T Spaces: Topological spaces with certain properties related to the T separation axiom.
• i=0,1,2: Different levels of separation and their associated properties.
10. Semi-Regular, Almost Regular, Almost Completely Regular, Semi-Normal, Almost Normal Spaces:
• Spaces that satisfy particular separation properties have varying degrees of regularity.
11. Regular Closed Functions and Hausdorff Spaces:
• Functions that preserve certain types of sets and spaces satisfy the Hausdorff separation axiom.
12. Irresolute and Almost Irresolute Functions:
• Functions that are nearly irresolute or satisfy a weaker form of irresolution.
13. s-Weakly Hausdorff Spaces, s-Normal, s-Regular Spaces and Their Properties:
• Spaces that satisfy certain properties related to weak forms of separation and regularity.

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