Intersection of two open sets is open | Real Analysis | Open sets | Metric Space | Topology | msc

Intersection of two open sets is open | Theorem | Msc | BSC | NET | NBHM | LPU | DU | IIT JAM | TIFR | Metric Space | NBD | Distance Function | Real analysis | Basic Topology | Math Tutorials.
--------Definition of Open set--------------------
        Video
--------Definition of Neighbourhood of a point ------------
       Video
--------Union of two NBDS is NBD---------
        Video
---------Intersection of NBDS is NBD--------------
       Intersection of NBDS is NBD | neighbo...
--------Superset of a NBD is also a NBD---------------------
       Video

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 2--------------
      Metric space/Distance Function | axio...
--------Metric space | Distance Function | Example 1--------------
     Video
-------Metric space : Definition and Axioms---------
     Metric space/Distance Function | Defi...

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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



















































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