Metamath Proof Explorer


Theorem kqf

Description: The Kolmogorov quotient is a topology on the quotient set. (Contributed by Mario Carneiro, 25-Aug-2015)

Ref Expression
Assertion kqf KQ : Top Kol2

Proof

Step Hyp Ref Expression
1 ovex j qTop x j y j | x y V
2 df-kq KQ = j Top j qTop x j y j | x y
3 1 2 fnmpti KQ Fn Top
4 kqt0 x Top KQ x Kol2
5 4 biimpi x Top KQ x Kol2
6 5 rgen x Top KQ x Kol2
7 ffnfv KQ : Top Kol2 KQ Fn Top x Top KQ x Kol2
8 3 6 7 mpbir2an KQ : Top Kol2