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Definition df-lp 20692
Description: Define a function on topologies whose value is the set of limit points of the subsets of the base set. See lpval 20695. (Contributed by NM, 10-Feb-2007.)
Assertion
Ref Expression
df-lp limPt = (𝑗 ∈ Top ↦ (𝑥 ∈ 𝒫 𝑗 ↦ {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))}))
Distinct variable group:   𝑥,𝑗,𝑦

Detailed syntax breakdown of Definition df-lp
StepHypRef Expression
1 clp 20690 . 2 class limPt
2 vj . . 3 setvar 𝑗
3 ctop 20459 . . 3 class Top
4 vx . . . 4 setvar 𝑥
52cv 1473 . . . . . 6 class 𝑗
65cuni 4366 . . . . 5 class 𝑗
76cpw 4107 . . . 4 class 𝒫 𝑗
8 vy . . . . . . 7 setvar 𝑦
98cv 1473 . . . . . 6 class 𝑦
104cv 1473 . . . . . . . 8 class 𝑥
119csn 4124 . . . . . . . 8 class {𝑦}
1210, 11cdif 3536 . . . . . . 7 class (𝑥 ∖ {𝑦})
13 ccl 20574 . . . . . . . 8 class cls
145, 13cfv 5790 . . . . . . 7 class (cls‘𝑗)
1512, 14cfv 5790 . . . . . 6 class ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))
169, 15wcel 1976 . . . . 5 wff 𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))
1716, 8cab 2595 . . . 4 class {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))}
184, 7, 17cmpt 4637 . . 3 class (𝑥 ∈ 𝒫 𝑗 ↦ {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))})
192, 3, 18cmpt 4637 . 2 class (𝑗 ∈ Top ↦ (𝑥 ∈ 𝒫 𝑗 ↦ {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))}))
201, 19wceq 1474 1 wff limPt = (𝑗 ∈ Top ↦ (𝑥 ∈ 𝒫 𝑗 ↦ {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))}))
Colors of variables: wff setvar class
This definition is referenced by:  lpfval  20694
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