## Metric SpaceThis book Metric Space has been written for the students of various universities. In the earlier chapters, proof are given in considerable detail, as our subject unfolds through the successive chapters and the reader acquires experience in following abstract mathematical arguments, the proof become briefer and minor details are more and more left for the reader to fill in for himself. It is a basic principle in the study of mathematics, and one too seldom emphasised that a proof is not really understood until the stage is reached at which one can grasp it is a whole and see it as a single idea. In achieving this end much more is necessary than merely following the individual steps in the reasoning. Contents: Basic Concept of Set, Metric Space, Compactness. |

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The book contains whole pages that, apart from paragraph indexing, are almost perfect word for word copies of George F. Simmons, Introduction to Topology and Modern Analysis (Krieger reprint 2003 of McGraw-Hill, 1963). For example

Sharma Simmons

168 ----- 73

171 ----- 76

177 ----- 84

In the pages on display in Google books, I find no attribution of the source. I wonder if the rights to republish under another name have been purchased.

### Common terms and phrases

arbitrary element called Cauchy sequence closed interval closed sets closure compact metric space compact space complex numbers contains countable definition denoted disjoint equivalence class equivalence relation exists F is closed f is one-one f-image finite intersection property finite number finite set finite subcover function f functions defined G is open g o f given Hence f integer inverse function Let f limit point locally compact many-one mapping f mathematical induction natural numbers non-empty set number of elements offered paper open cover open intervals open set open subset ordered pairs partially ordered set positive integer product topology Proof rational numbers real function real line real number reflexive sequentially compact set of points Show that f Solution Sr(x subbase subspace symbol Theorem topological space triangle union of open