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…
Tag: Examples
Analysis/Topology: Connected Sets in Metric Spaces
A short discussion on Connected Sets in Metric Spaces with definition, examples, counterexamples, properties and quizzes.
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…
All About: Definition of Sets
A detailed discussion of #Definition of #Sets, including #examples, #counterexamples, #quizzes. Useful for #GRE #CSIR #JRF #NET #GATE #Mathematics Aspirants
Examples and Counterexampels: Abelian Groups
Examples and Counterexamples of Abelian Groups
Example and Counterexamples: Cyclic groups
Here are some important definitions, facts and examples of cyclic groups.
