Separation axioms - T0 space - T1 space - hausdorff space - regular space - normal space - Topology

OMG Maths
OMG Maths
47.4 هزار بار بازدید - 4 سال پیش - Separation axioms in topology |
Separation axioms in topology | Topology | Real Analysis | Topological space | Math Tutorials | Classes by Cheena Banga ***Separation axioms (pdf) : omgmaths.com/real-analysis/separation-axioms-topol… *****Real Analysis : Playlist****    • Real Analysis   T0 space | T1 space | T2 space | T3 space | T4 space | T5 space | Hausdorff Space | Regular Space | Tychonoff space useful for Msc | BSC | NET | NBHM | LPU | DU | IIT JAM | TIFR Other topics covered in playlist: Disconnectedness and connectedness theorems. Separated sets theorem Separated Sets | Definition | Examples | Real Analysis | Metric Space | Topology Separated sets are Disjoint. Disjoint sets may or may not be Separated. Cantor Set Perfect Set | Definition with example. Closed subset of a compact set is compact. Heine-Borel theorem Closed Set | definition | theorems set is closed iff its complement is open Bolzano weierstrass theorem : Every infinite bounded subset of R has a limit point. 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 Thanks for Watching Math Tutorials Classes by Cheena Banga 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
4 سال پیش در تاریخ 1399/10/17 منتشر شده است.
47,489 بـار بازدید شده
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