Differential Geometry | Topology Answers

Prove or disprove any metric defined on X(#0) induces a topology on X

Prove or disprove any metric defined on X(#0) induces a topology on X

Prove or disprove any metric defined on X(#0) induces a topology on X

Prove or disprove every topological space is metrizible

Let E be a Euclidian vector space, let (i,j) be its standard basis. Note C
the circle centered at the origin with radius a, where a is a real positive number. ⃗⃗
1. Let δ = (a cos as )i+(a sin as )j. Show that ([0, 2πa], δ) is a unit speed parametrization of C

Prove that the boundary of a subset A of a metric space X is always a closed set

Prove or disprove any metric defined on X(#0) induces a topology on X

Prove or disprove every topological space is metrizible

2.A stone moves along the path x=t^3+1,y=t^3, z=2t+5, where t denote time. What is the component of (dp)/dt ?
3i+2j-2k
3i-2j+2k
3i+2j+2k
-3i+2j+2k

Show that the set of rational numbers with the subspace topology of R is disconnected