1)Prove that the intersection of an arbitrary collection of
closed sets is closed.
2)Prove that the union of a finite collection of closed sets is
closed
Differential Geometry ( Work Shop for Test 1)
(5) Prove that a regular curve (i.e., curve with positive
curvature at all points) is a helix iff the ratio of the torsion to
curvature is a constant. please use Differential Geometry Form not
Calculus.
1. Use the ε-δ definition of continuity to prove that (a) f(x) =
x 2 is continuous at every x0. (b) f(x) = 1/x is continuous at
every x0 not equal to 0.
3. Let f(x) = ( x, x ∈ Q 0, x /∈ Q (a) Prove that f is
discontinuous at every x0 not equal to 0. (b) Is f continuous at x0
= 0 ? Give an answer and then prove it.
4. Let f and g...
Give Examples (this is complex analysis):
(a.) First characterize open and closed sets in terms of their
boundary points. Then give two examples of sets satisfying the
given condition: one set that is bounded (meaning that there is
some real number R > 0 such that |z| is greater than or equal to
R for every z in S), and one that is not bounded. Give your answer
in set builder notation. Finally, choose one of your two examples
and...
Differential Geometry (Mixed Use of Vector Calculus & Linear
Algebra)
1A. Prove that if p=(x,y) is in the set where y<x and if
r=distance from p to the line y=x then the ball about p of radius r
does not intersect with the line y=x.
1B. Prove that the set where y<c is an open set.
"•“"Suppose ℱ, ?1, and ?2 are nonempty families of sets. Prove
that if ℱ ⊆ ?1 ∩ ?2, then ∩?1 ∪ ∩?2 ⊆ ∩ℱ.“"
Please explain what the question is asking for and break down
the solution for me step by step with explanations please!