Ways to “compress” a topology!
The definition of topological spaces and some interesting examples and counterexamples of topological spaces!
A series to quickly revise Topology – Dedicated to my students.
An intuitive introduction to topology/quickly revise the paper after a semester of coursework.
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…
A short discussion on Connected Sets in Metric Spaces with definition, examples, counterexamples, properties and quizzes.
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…
Here’s a video discussing a few simple examples of metric spaces.
Here’s a video discussing the definition of metric spaces, and the inspiration behind it. Rarely
Examples and Counterexamples: Real Line with Discrete Metric/Topology. Did you try the challenges at the end? Leave your thoughts in the comments below!