====== Topology: Handwritten Notes ======
{{ :notes:topology-house.jpg?nolink&600|House of Tau}}
A topological space is a collection of points with a topology-a structure that describes how close two points are to one another. It is a generalisation of Euclidean spaces that makes it possible to investigate boundaries, continuity, and connectivity. A topology is a group of open sets, or subsets, that adhere to certain principles.

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  |Mr. Tahir Mahmood  |
^ Pages  |262 pages  |
^ Format  |Scanned PDF  | 
^ Size  |10.08 mB  |

==== What is in the notes?====
<grid>
<col sm="6">
  *  Metric space
  *  Minkowski's inequality
  *  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's intersection theorem
  *  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>
<col sm="6">
  *  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; Totally bounded
  *  Connected spaces; Disconnected
  *  Component
  *  Totally disconnected
  *  Separated
  *  Normed spaced
  *  Uniformly continuous
  *  Closed unit ball; Convex set
  *  Vector space
  *  Linear combination; Spanning set; Linearly independent
  *  Linearly dependent
  *  Linearly independent lemma
  *  Finite dimensional; Subspace
  *  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's inequality
  *  Total orthonormal sets (definition); Parsevel's equality
  *  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
 </col>
</grid>

{{include>msc-notes-viewer.php}}

==== Download or View online ====
<callout type="success" icon="fa fa-download">
  * {{ :notes:topology-handwritten-notes.pdf |Download PDF}} | <btn type="primary" size="xs" modal="modal-thn">View Online</btn>
<modal id="modal-thn" size="lg" title="Topology: Handwritten Notes">
{{gview noreference>:notes:topology-handwritten-notes.pdf}}
</modal> 
</callout>
====There are more notes on the topology====
{{topic>Topology&simplelist}}
{{tag>MSc BS Notes Topology}}