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Definition df-ntr 20872
Description: Define a function on topologies whose value is the interior function on the subsets of the base set. See ntrval 20888. (Contributed by NM, 10-Sep-2006.)
Assertion
Ref Expression
df-ntr int = (𝑗 ∈ Top ↦ (𝑥 ∈ 𝒫 𝑗 (𝑗 ∩ 𝒫 𝑥)))
Distinct variable group:   𝑥,𝑗

Detailed syntax breakdown of Definition df-ntr
StepHypRef Expression
1 cnt 20869 . 2 class int
2 vj . . 3 setvar 𝑗
3 ctop 20746 . . 3 class Top
4 vx . . . 4 setvar 𝑥
52cv 1522 . . . . . 6 class 𝑗
65cuni 4468 . . . . 5 class 𝑗
76cpw 4191 . . . 4 class 𝒫 𝑗
84cv 1522 . . . . . . 7 class 𝑥
98cpw 4191 . . . . . 6 class 𝒫 𝑥
105, 9cin 3606 . . . . 5 class (𝑗 ∩ 𝒫 𝑥)
1110cuni 4468 . . . 4 class (𝑗 ∩ 𝒫 𝑥)
124, 7, 11cmpt 4762 . . 3 class (𝑥 ∈ 𝒫 𝑗 (𝑗 ∩ 𝒫 𝑥))
132, 3, 12cmpt 4762 . 2 class (𝑗 ∈ Top ↦ (𝑥 ∈ 𝒫 𝑗 (𝑗 ∩ 𝒫 𝑥)))
141, 13wceq 1523 1 wff int = (𝑗 ∈ Top ↦ (𝑥 ∈ 𝒫 𝑗 (𝑗 ∩ 𝒫 𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  ntrfval  20876
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