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Definition df-hmeo 12484
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
StepHypRef Expression
1 chmeo 12483 . 2 class Homeo
2 vj . . 3 setvar 𝑗
3 vk . . 3 setvar 𝑘
4 ctop 12178 . . 3 class Top
5 vf . . . . . . 7 setvar 𝑓
65cv 1330 . . . . . 6 class 𝑓
76ccnv 4538 . . . . 5 class 𝑓
83cv 1330 . . . . . 6 class 𝑘
92cv 1330 . . . . . 6 class 𝑗
10 ccn 12368 . . . . . 6 class Cn
118, 9, 10co 5774 . . . . 5 class (𝑘 Cn 𝑗)
127, 11wcel 1480 . . . 4 wff 𝑓 ∈ (𝑘 Cn 𝑗)
139, 8, 10co 5774 . . . 4 class (𝑗 Cn 𝑘)
1412, 5, 13crab 2420 . . 3 class {𝑓 ∈ (𝑗 Cn 𝑘) ∣ 𝑓 ∈ (𝑘 Cn 𝑗)}
152, 3, 4, 4, 14cmpo 5776 . 2 class (𝑗 ∈ Top, 𝑘 ∈ Top ↦ {𝑓 ∈ (𝑗 Cn 𝑘) ∣ 𝑓 ∈ (𝑘 Cn 𝑗)})
161, 15wceq 1331 1 wff Homeo = (𝑗 ∈ Top, 𝑘 ∈ Top ↦ {𝑓 ∈ (𝑗 Cn 𝑘) ∣ 𝑓 ∈ (𝑘 Cn 𝑗)})
Colors of variables: wff set class
This definition is referenced by:  hmeofn  12485  hmeofvalg  12486  ishmeo  12487
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