i recently learned about topologies and i just thought of an incredibly cursed one

the topology of topologies

start with an underlying set K
declare the set P(K) of subsets of K

T(K) is the set consisting only of subsets of P(K) that satisfy the axioms needed to be a topology defined by a set of open sets (i.e. for any element t in T(K), K and the empty set belong to t and t is closed under union and intersection)

now we can define our cursed topology
its underlying set of points is T(K)
and its set of open sets is the union, for every nonempty set M of subsets of K, of the set of subsets of T(K) where every element r of said subset is a superset of M

if i've constructed this right, it's a topology whose individual points are topologies of K, and where closeness in the supertopology represents sharing open sets in common