I think the language and machinery of topology, even when just reconstructing the language of sets in a discrete setting, highlights interesting facets of numbers.
eg, if you look at the inverse image of various mappings, and particularly in cases where you can iterate this via a function from a set into itself, you can start building up meaningful comments on certain classes of number theory problems.
But I am curious what you mean by "prime ideals of integers localized at some prime", since I know what (prime) ideals are, but am not sure I follow what you mean by localized
I think the language and machinery of topology, even when just reconstructing the language of sets in a discrete setting, highlights interesting facets of numbers.
eg, if you look at the inverse image of various mappings, and particularly in cases where you can iterate this via a function from a set into itself, you can start building up meaningful comments on certain classes of number theory problems.
But I am curious what you mean by "prime ideals of integers localized at some prime", since I know what (prime) ideals are, but am not sure I follow what you mean by localized