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Definition df-lp 21679
 Description: Define a function on topologies whose value is the set of limit points of the subsets of the base set. See lpval 21682. (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 21677 . 2 class limPt
2 vj . . 3 setvar 𝑗
3 ctop 21436 . . 3 class Top
4 vx . . . 4 setvar 𝑥
52cv 1529 . . . . . 6 class 𝑗
65cuni 4837 . . . . 5 class 𝑗
76cpw 4542 . . . 4 class 𝒫 𝑗
8 vy . . . . . . 7 setvar 𝑦
98cv 1529 . . . . . 6 class 𝑦
104cv 1529 . . . . . . . 8 class 𝑥
119csn 4564 . . . . . . . 8 class {𝑦}
1210, 11cdif 3937 . . . . . . 7 class (𝑥 ∖ {𝑦})
13 ccl 21561 . . . . . . . 8 class cls
145, 13cfv 6354 . . . . . . 7 class (cls‘𝑗)
1512, 14cfv 6354 . . . . . 6 class ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))
169, 15wcel 2107 . . . . 5 wff 𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))
1716, 8cab 2804 . . . 4 class {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))}
184, 7, 17cmpt 5143 . . 3 class (𝑥 ∈ 𝒫 𝑗 ↦ {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))})
192, 3, 18cmpt 5143 . 2 class (𝑗 ∈ Top ↦ (𝑥 ∈ 𝒫 𝑗 ↦ {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))}))
201, 19wceq 1530 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  21681
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