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Definition df-lp 21154
Description: Define a function on topologies whose value is the set of limit points of the subsets of the base set. See lpval 21157. (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 21152 . 2 class limPt
2 vj . . 3 setvar 𝑗
3 ctop 20911 . . 3 class Top
4 vx . . . 4 setvar 𝑥
52cv 1636 . . . . . 6 class 𝑗
65cuni 4630 . . . . 5 class 𝑗
76cpw 4351 . . . 4 class 𝒫 𝑗
8 vy . . . . . . 7 setvar 𝑦
98cv 1636 . . . . . 6 class 𝑦
104cv 1636 . . . . . . . 8 class 𝑥
119csn 4370 . . . . . . . 8 class {𝑦}
1210, 11cdif 3766 . . . . . . 7 class (𝑥 ∖ {𝑦})
13 ccl 21036 . . . . . . . 8 class cls
145, 13cfv 6101 . . . . . . 7 class (cls‘𝑗)
1512, 14cfv 6101 . . . . . 6 class ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))
169, 15wcel 2156 . . . . 5 wff 𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))
1716, 8cab 2792 . . . 4 class {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))}
184, 7, 17cmpt 4923 . . 3 class (𝑥 ∈ 𝒫 𝑗 ↦ {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))})
192, 3, 18cmpt 4923 . 2 class (𝑗 ∈ Top ↦ (𝑥 ∈ 𝒫 𝑗 ↦ {𝑦𝑦 ∈ ((cls‘𝑗)‘(𝑥 ∖ {𝑦}))}))
201, 19wceq 1637 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  21156
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