Question

If A is not totally bounded, show that A has an infinite subset B that is homeomorphic to a discrete space (where B is supplied with its relative metric). [Hint: Find epsilon>0 and a sequence (x_{n}) in A such that d(x_{n}, x_{m}) >= epsilon for n not equal to m . How does this help?]

Answer 1

Answer:

Just show that {xn:n∈N} is discrete, i.e. every singleton is an open set.

For each n∈N, show that B(xn,ϵ) only contains xn.

Answer 2

Answer:

light is most powerful and fastest in universe we can do time travel by the speed of light