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:

**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.

**Semi-Open, Semi-Closed Mappings:**- Mappings that preserve semi-open or semi-closed sets under inverse image.

**Almost Closed and Almost Open Mappings:**- Mappings that are nearly closed or nearly open, preserving certain properties.

**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.

**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.

**Weakly Continuous and Almost Continuous Mappings:**- Mappings that are nearly continuous or satisfy a weaker form of continuity.

**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.

**Strongly Continuous Mapping:****Strongly Continuous Mapping:**A more stringent form of continuity.

**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.

**Semi-Regular, Almost Regular, Almost Completely Regular, Semi-Normal, Almost Normal Spaces:**- Spaces that satisfy particular separation properties have varying degrees of regularity.

**Regular Closed Functions and Hausdorff Spaces:**- Functions that preserve certain types of sets and spaces satisfy the Hausdorff separation axiom.

**Irresolute and Almost Irresolute Functions:**- Functions that are nearly irresolute or satisfy a weaker form of irresolution.

**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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Advanced Topology-1