Bolzano weierstrass theorem | Real analysis | Metric Space | Basic Topology | limit point | Msc |bsc

Bolzano weierstrass theorem | Limit Point of a set | definition | Theorem | Msc | BSC | NET | NBHM | LPU | DU | IIT JAM | TIFR | Metric Space | NBD | Distance Function | Real analysis | Basic Topology | Math Tutorials.
State: Every infinite bounded subset of R has a limit point.
Limit point of a set | definition | Limit/cluster/accumulation point.
   • Limit/cluster/accumulation point | De...  
Other topics covered in playlist:
Definition of Neighbourhood of a point
Definition of Open set
infinite intersection of open sets need not to be open
Union of two NBDS is NBD
Intersection of NBDS is NBD
Superset of a NBD is also a NBD
Every Open interval (a,b) is neighbourhood of each of its points.
Closed interval is neighbourhood of each point except end points.
real numbers is NBD of each real number
Rational numbers set is not the neighbourhood of any of its points.
Metric space | Distance Function | Example
Metric space : Definition and Axioms
Real Analysis : Introduction and Intervals
Union of countable sets is countable
Finite,infinite,equivalent,denumerable,countable sets
Infinite subset of countable set is countable
Field,Ordered Field,complete Ordered Field
Set of Integers is Countable
Supremum and infimum
Set is countably infinite iff it can be written in the form distinct elements
Continuum Hypothesis
Cartesian product of two countable sets is Countable
Set of Rational numbers is Countable


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Definition of metric Space
Examples of metric space
Open and Closed sets
Topology and convergence
Types of metric spaces
Complete Spaces
Bounded and complete bounded spaces
Compact spaces
Locally compact and proper spaces
connectedness
Separable spaces
Pointed Metric spaces
Types of maps between metric spaces
continuous maps
uniformly continuous maps
Lipschitz-continuous maps and contractions
isometries
Quasi-isometries
notions of metric space equivalence
Topological properties
Distance between points and sets
Hausdorff distance and Gromov metric
Product metric spaces
Continuity of distance
Quotient metric spaces
Generalizations of metric spaces
Metric spaces as enriched categories



















































Basic Topology
Topology mathematics
topology maths
Topology optimization
Topology lecture
Topology and types
Topology axioms














Real analysis for BA maths
Real analysis for MA Maths
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Real Analysis Basic Concept


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bounded intervals on the real number line
bounded and unbounded intervals
Denumerable union of Denumerable set is Denumerable
Denumerable union of Denumerable sets is Denumerable
union of Denumerable sets is Denumerable
a Denumerable union of Denumerable sets is Denumerable
a countable union of countable sets is countable


discrete math
countable sets examples
countable sets and uncountable sets
countable sets in real analysis
countable sets proof
countable sets problems
countable and uncountable sets discrete mathematics
countable set in real analysis
countable and uncountable sets in discrete mathematics
what is countable and uncountable sets

finite sets and infinite sets
finite sets meaning
finite sets definition
examples of finite sets(mathematics)