General Topology

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Description: Th branch of Topology most relevant to Modern Analysis is called Point Set Topology or General Topology and hence plays a prominent role in many branches of Mathematics.
Topics for "General Topology"

01. Topological Spaces

Definition of Topology
Indiscrete and Discrete Topology
Coarser and Finer Topology
Intersection of Topologies
Open Subset of a Topological Space
Closed Subset of a Topological Space
Usual Topology on Real
Cofinite Topology
Subspaces of Topology
Limit Point of a Set
Isolated Point of a Set
Closure of a Set
Neighbourhood of a Point
Interior Point of a Set
Exterior Point of a Set
Boundary Point of a Set

02. Bases and Subbases

Base or Open Base of a Topology
Subbase for a Topology
Local Base for a Topology
First Countable Space
Second Countable Space
Lindelof Space
Separable Space
Continuity in Topological Spaces
Open Mapping and Closed Mapping
Homeomorphism
Topological Property
Product Topology

03. Separation Axioms

T0 Space
T1 Space
T2 Space or Hausdorff Space
Regular Space
Completely Regular Space
Normal Space

04. Connectedness and Compactness

Disconnected Space
Connected Space
Components of a Space
Totally Disconnected Space
Some Applications of Connectedness
Compact Space
Finite Intersection Property
Local Compact