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| - | ====== Topology: Handwritten Notes ====== | ||
| - | A handwritten notes of Topology by Mr. Tahir Mehmood. These notes covers almost every topic which required to learn for MSc mathematics. | ||
| - | {{ : | ||
| - | ^ Name |Topology: Handwritten Notes | | ||
| - | ^ Author | ||
| - | ^ Pages |262 pages | | ||
| - | ^ Format | ||
| - | ^ Size |10.08 mB | | ||
| - | ==== Contents & Summary==== | ||
| - | < | ||
| - | <col sm=" | ||
| - | * Metric space | ||
| - | * Minkowski' | ||
| - | * Open set | ||
| - | * Closed ball | ||
| - | * Closed set | ||
| - | * Bounded set | ||
| - | * Limit point | ||
| - | * Closure of a set | ||
| - | * Convergence in metric space and complete metric space | ||
| - | * Cauchy sequence | ||
| - | * Bounded sequence | ||
| - | * Nested interval property or Cantor' | ||
| - | * Continuous function | ||
| - | * Topological spaces | ||
| - | * Metric topology, cofinite topology | ||
| - | * Open set | ||
| - | * Closed set | ||
| - | * Closure of a set | ||
| - | * Neighbourhood | ||
| - | * Interior point, exterior point | ||
| - | * Boundary point | ||
| - | * Limit point (with respect to topology) | ||
| - | * Isolated point | ||
| - | * Dense | ||
| - | * Separable set; Countable set | ||
| - | * Base of topology | ||
| - | * Neighbourhood base or local base or base at a point | ||
| - | * Open cover; Lindelof space | ||
| - | * Lindelof theorem | ||
| - | * Relative topology, subspace | ||
| - | * Separation axioms; $T_0$-space | ||
| - | * $T_1$-space | ||
| - | * Subbase; Generation of topologies | ||
| - | * $T_2$-space | ||
| - | * Continuous function (with respect to topologies) | ||
| - | * Product topology | ||
| - | * Convergence of sequence in topological spaces | ||
| - | </ | ||
| - | <col sm=" | ||
| - | * Regular space | ||
| - | * Completely regular space | ||
| - | * Compactness in topological spaces | ||
| - | * Homeomorphism | ||
| - | * Countably compact space | ||
| - | * Bolzano Weierstrass property | ||
| - | * Lebesgue number; Big set; Lebesgue covery lemma | ||
| - | * $\varepsilon-$net; | ||
| - | * Connected spaces; Disconnected | ||
| - | * Component | ||
| - | * Totally disconnected | ||
| - | * Separated | ||
| - | * Normed spaced | ||
| - | * Uniformly continuous | ||
| - | * Closed unit ball; Convex set | ||
| - | * Vector space | ||
| - | * Linear combination; | ||
| - | * Linearly dependent | ||
| - | * Linearly independent lemma | ||
| - | * Finite dimensional; | ||
| - | * Equivalent norms | ||
| - | * Banach space | ||
| - | * Reiz Lemma | ||
| - | * Hilbert spaces; Inner product spaces | ||
| - | * Polarization identity | ||
| - | * Cauchy Schewarz inequality | ||
| - | * Appalonius identity | ||
| - | * Hilbert space; Pythagorian theorem | ||
| - | * Minimizing vector | ||
| - | * Direct sum | ||
| - | * Orthogonal set; Orthonormal set | ||
| - | * Bessel' | ||
| - | * Total orthonormal sets (definition); | ||
| - | * Linear Operator; The Kernel or Null space of a linear operator; Continuous linear operator | ||
| - | * Bounded linear operator | ||
| - | * Norm of a bounded lienar operator | ||
| - | * Linear functionals | ||
| - | </ | ||
| - | </ | ||
| - | |||
| - | {{include> | ||
| - | |||
| - | ==== Download or View online ==== | ||
| - | <callout type=" | ||
| - | * {{ : | ||
| - | <modal id=" | ||
| - | {{gview noreference>: | ||
| - | **{{: | ||
| - | </ | ||
| - | </ | ||
| - | ====Notes of other subjects==== | ||
| - | {{topic> | ||
| - | {{tag> | ||