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Definition df-perf 20693
Description: Define the class of all perfect spaces. A perfect space is one for which every point in the set is a limit point of the whole space. (Contributed by Mario Carneiro, 24-Dec-2016.)
Assertion
Ref Expression
df-perf Perf = {𝑗 ∈ Top ∣ ((limPt‘𝑗)‘ 𝑗) = 𝑗}

Detailed syntax breakdown of Definition df-perf
StepHypRef Expression
1 cperf 20691 . 2 class Perf
2 vj . . . . . . 7 setvar 𝑗
32cv 1473 . . . . . 6 class 𝑗
43cuni 4366 . . . . 5 class 𝑗
5 clp 20690 . . . . . 6 class limPt
63, 5cfv 5790 . . . . 5 class (limPt‘𝑗)
74, 6cfv 5790 . . . 4 class ((limPt‘𝑗)‘ 𝑗)
87, 4wceq 1474 . . 3 wff ((limPt‘𝑗)‘ 𝑗) = 𝑗
9 ctop 20459 . . 3 class Top
108, 2, 9crab 2899 . 2 class {𝑗 ∈ Top ∣ ((limPt‘𝑗)‘ 𝑗) = 𝑗}
111, 10wceq 1474 1 wff Perf = {𝑗 ∈ Top ∣ ((limPt‘𝑗)‘ 𝑗) = 𝑗}
Colors of variables: wff setvar class
This definition is referenced by:  isperf  20707
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