Topology And Metric Space Hand Written Note By PI AIM INSTITUTE

Here, We provided to Best Topology And Metric Space Hand Written Note. Topology And Metric Space gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces, and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis. Free download PDF Best Topology And Metric Space Hand Written Note.

topology and metric space hand written noteIn mathematics, a metric space is a set for which distances between all members of the set are defined. Those distances, taken together, are called a metric on the set. A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces. Free download PDF Best Topology And Metric Space Hand Written Note.

In this second revised and enlarged edition, based on the extensive feedback sent by the readers, some material has been removed, some new material included and nearly all problems are given comments, hints, and solutions. Free download PDF Best Topology And Metric Space Hand Written Note.

Table Of Contents:

  • Preface 
  • Basic Notions 
  • Convergence 
  • Continuity 
  • Compactness 
  • Connectedness 
  • Complete Metric Spaces 
  • Answers, Hints, and Solutions 
  • Bibliography 
  • Index.






The most familiar metric space is 3-dimensional Euclidean space. In fact, a “metric” is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line segment connecting them. Free download PDF Best Topology And Metric Space Hand Written Note. Other metric spaces occur for example in elliptic geometry and hyperbolic geometry, where distance on a sphere measured by an angle is a metric, and the hyperboloid model of hyperbolic geometry is used by special relativity as a metric space of velocities.

Key Features:

  • All concepts introduced using the primitive concepts of open balls or open sets
  • Geometric motivations of concepts, definitions, and results
  • Real-life motivations and analogies
  • Lots of concrete and geometric examples and pictures
  • Numerous exercises in meaningful contexts, with copious hints to most of them
  • Typical applications of major results
  • Attention to the difficulties faced by beginners
  • Most of the proofs start with the strategy of the proof so as to enable good students 
  • to work on their own
  • Prepares the ground for higher aspects of topology and analysis.


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