Differential Geometry | Topology Answers

Prove that the unit n-cube Iⁿ is a compact subset of Rⁿ

State and prove Gluing lemma

Prove that the fixed point property is a topological invariant

If Y is a connected subspace of a space X ,then prove that Y closure is connected

Let X be a connected space and f:X to Y a continuous function from X onto a space Y .prove that Y is connected

Find the unit tangent vector at the point 2,0,pi for a curve which is described by the parametric equations

x=2Sina y=3cosa z=2a

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