which of the following topologies are metrizable?

[math25]

Hi, can someone please help me to determine which of the following topologies are metrizable?

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