- #1

math25

- 25

- 0

a)Let X be any inf nite set and let T = {U subset of X : x\u is finite }

b) Let X = R and let T = {U subset of R : R \ U is FI nite of countable }

c) For each k in N, let Nk = {1; 2,...,K} . Let T = {empty set} U{N}U {Nk: k is in N}

d) For each k in N, let U = { k; k + 1; k + 2;...} then T = { empty set} U {Uk : k is in N}

e) Let T = {empty set} U { R} U { (a, infinity) : a is in R}

I think that {e} is not metrizable (weak topology and not countable)

Also, I think that a) and b) are metrizable , however not sure about c) and d)

thanks