Quick Revision: Topology (Part 0)

A series to quickly revise Topology – Dedicated to my students.

Analysis/Topology: Bounded and Totally Bounded Sets

Definitions Bounded set: Let <M,ρ> be a metric space. We say that the subset A of M is bounded if there exists a positive number L such that ρ(x,y)≤L  (x,y∈A) (Wikipedia) Diameter of a set: If A is bounded, we define diameter of A (denoted by diam A) as diam A=  ρ(x,y). If A is not…

Topology/Analysis: Homeomorphism

Definition If is one-one and onto (1-1 correspondence/bijection) continuous is continuous Then we call a homeomorphism between two metric spaces . The metric space  are said to be homeomorphic. Properties and Theorems If f is a homeomorphism between metric spaces , The set G⊂ is open if and only if the image f(G)⊂ is open. The…

CSIR-NET: Analysis/Topology Quiz 1

CSIR-NET December 2015, Part B Question. How should I analyze this question when I am preparing for CSIR-NET? Mark all mathematical terms here. Read their definitions. Try construct examples for each terms, try apply it in options. This question is interesting because it talks about a lot of mathematical terms, but the keyword is nowhere…