Differential Geometry | Topology Answers

find curvature r = (4/5 Cost, 1-sint, -3/2 Cost)

Find Torison r=(a (3u, u³), 3au², 3a (3u+u³)

Prove that

gamma=(a(3u,u^ 8 ), 3a * u ^ 2, 3a * (3u + u ^ 3)

tau = 1/(k ^ 2) * (r*gamma)

Find curvature r(t) = ( ½ Cost, 1-sint, -3/2 cost)

iii) find curvature r(t) = ( ½ Cost, 1-sint, -3/2 cost)

Find the level curve each of function at indicated point? (a) 𝒇(𝒙, 𝒚) = 𝒙 𝟐 − 𝒚 𝟐 , 𝒂𝒕 𝒄 = 𝟏. (b) 𝒈(𝒙, 𝒚) = 𝒆 𝒙𝒚 , 𝒂𝒕 𝒄 = 𝟎. 𝟓, 𝟑. (c) 𝒉(𝒙, 𝒚) = 𝒍𝒏 (𝒙 𝟐 + 𝒚 𝟐 ) 𝒂𝒕 𝒄 = −𝟏, 𝟎, 𝟏. 

if x={1,2,3,4} suppose that Σ={{1},{1,2},{2,3,4},{1,2,3}}, what is T(Σ)?

The Euclidean space p² is metric space . Specially R^' (real line) R²( the complex plane) etc are metric .

Let X be a metric space ,then show that

(a) A subset F of X is closed iff F^c is open .

(b) A subset E of X is open iff E^c is closed .