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Definition of Separated sets. If A & B are open disjoint set then they are Separated.

Finite Intersection property

Continuous image of compact metric space is compact

A subset of R is compact if and only if it is closed and bounded.

Any compact subset of metric space is closed and bounded.

A compact metric space has B.W.P.

Sequential compactness & Bolzano Weirerstrass Property

Finite subset of discrete metric space is compact.

Compactness Definitions of Open cover & finite Subcover

Absolute Maximum absolute Minimum Location of root theorem

Examples on Continuity

Examples on Continuity

Continuity ,Sequential criteria for continuity

Examples on Limit

A function from a metric space to another is continuous iff inverse image of open set is open.

Examples on Continuous function

Continuous function Definition & Examples

Examples on Limits

Examples on Divergence criteria

Sequential criteria for Limits

Uniqueness of limit

Definitions of Odd & Even function

Dense set

Range of a function and definition of some functions