Differential Geometry | Topology Answers

Give an example of a projection. Which is not closed

Prove that the real line is a homeomorphic to the interval (0,1) with the subspace topology

Give an example of a nowhere dense set in a metric space .substantiate your claim

Given a metric d on a set X prove that there exists an equivalent bounded metric d' on X

Prove that set of all open subsets of a metric space is a topology

Find the envelope of the family of the curves

1) y=3px-p^3

Where p=parameter

2) y=mx-2am-am^3

Where m=parameter

if v=2ti+t^2j+tk,find the position vector r of the particle at t=1 given that the particle initially was at i+2j+2k