Differential Geometry | Topology Answers

Let (x,d) be metric space with the discrete metric .prove that every subset of X is open

Let (x,d) be metric space and A proper subset of X .Define the closure of a set A .consider the usual metric space (R^n,d) .let A = {(x₁,x₂,.......x_n): x_i element of Q}

Define a metric space .Give an example of a metric space

Give an example of a metric space which is not compact

Prove or disprove : A continuous bijection is a homeomorphism

Give an example of a first countable space which is not second countable ,substantiate your claim

Establish a.necessary and sufficient condition for a.family of subsets of a set X to be a.Q base for a topology on X