In the lecture, our prof. mentioned that the correspondence between nets and filters is a Galois correspondence without giving any more details about that.
In algebra, the proof of the Galois correspondence theorem we compared orders of the fixed field of H-automorphism and the order of the subgroup H and concluded that they must be equal due to the fact that the order is finite.
How can I think of a Galois correspondence of filters and nets? What are their groups, if there are any. If there are, what gives the finiteness in this correspondence?