sure.

here is an extreme example:

let τ = 2^{X}, the power set of X. in this topology EVERY subset of X is open (this is called the discrete topology on X).

let σ = {Ø,X}. here there are only TWO open sets, the empty set, and X itself (this is called the indiscrete topology on X).

if X contains more than one element, then the set {x} for a single element of X, is open in the first, but not in the second.