Real analysis Part 1_ Basic Topology

Real analysis Part 1_ Basic Topology free download

Basic Topology, Countable Sets, Perfect sets, Limit Points, Open sets, Neighborhood, Interior points, closed sets

Course Introduction:

In the mathematics world, Real analysis is the branch of mathematics analysis that studies the behavior of real numbers, sequences and series of real number and real-valued function. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiation, and integrability.

Key content of the course:

• Basic Topology introduction to sets

• Concept of One one mapping, Onto mapping, Injective and surjective mappings

• Countable sets, uncountable sets and  atmost countable sets with examples.

• Definition and Theorems on countable sets and uncountable sets

• Definition of Open sets and closed sets

• Intersection and union of sets and theorem based on intersection and union of closed and open set

• Definition of Neighborhood of a point

• Detailed explanation and theorems on Neighborhood of point

• Theorems on Open sets and closed sets and Clopen sets

• Definition of Limit points, Interior points, exterior points

• Theorems and examples on limit points, interior points and exterior points

• Dense sets and Theorems on Dense sets

• Definition and concept of Perfect sets

• Theorems on perfect sets

• Bolzano Weierstrass theorem

• Heine Borel theorems including all expected Theorems, Assignments and Examples of above contents.

So enroll the course and explore the content. See you on the course!