Definition df-hmeo 12941

Description: Function returning all the homeomorphisms from topology 𝑗 to topology 𝑘. (Contributed by FL, 14-Feb-2007.)

Assertion

Ref	Expression
df-hmeo	⊢ Homeo = (𝑗 ∈ Top, 𝑘 ∈ Top ↦ {𝑓 ∈ (𝑗 Cn 𝑘) ∣ ◡𝑓 ∈ (𝑘 Cn 𝑗)})

Distinct variable group:   𝑓,𝑗,𝑘

Detailed syntax breakdown of Definition df-hmeo

Step	Hyp	Ref	Expression
1		chmeo 12940	. 2 class Homeo
2		vj	. . 3 setvar 𝑗
3		vk	. . 3 setvar 𝑘
4		ctop 12635	. . 3 class Top
5		vf	. . . . . . 7 setvar 𝑓
6	5	cv 1342	. . . . . 6 class 𝑓
7	6	ccnv 4603	. . . . 5 class ◡𝑓
8	3	cv 1342	. . . . . 6 class 𝑘
9	2	cv 1342	. . . . . 6 class 𝑗
10		ccn 12825	. . . . . 6 class Cn
11	8, 9, 10	co 5842	. . . . 5 class (𝑘 Cn 𝑗)
12	7, 11	wcel 2136	. . . 4 wff ◡𝑓 ∈ (𝑘 Cn 𝑗)
13	9, 8, 10	co 5842	. . . 4 class (𝑗 Cn 𝑘)
14	12, 5, 13	crab 2448	. . 3 class {𝑓 ∈ (𝑗 Cn 𝑘) ∣ ◡𝑓 ∈ (𝑘 Cn 𝑗)}
15	2, 3, 4, 4, 14	cmpo 5844	. 2 class (𝑗 ∈ Top, 𝑘 ∈ Top ↦ {𝑓 ∈ (𝑗 Cn 𝑘) ∣ ◡𝑓 ∈ (𝑘 Cn 𝑗)})
16	1, 15	wceq 1343	1 wff Homeo = (𝑗 ∈ Top, 𝑘 ∈ Top ↦ {𝑓 ∈ (𝑗 Cn 𝑘) ∣ ◡𝑓 ∈ (𝑘 Cn 𝑗)})

This definition is referenced by:  hmeofn  12942  hmeofvalg  12943  ishmeo  12944