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Definition df-topgen 15875
Description: Define a function that converts a basis to its corresponding topology. Equivalent to the definition of a topology generated by a basis in [Munkres] p. 78 (see tgval2 20518). See tgval3 20525 for an alternate expression for the value. (Contributed by NM, 16-Jul-2006.)
Assertion
Ref Expression
df-topgen topGen = (𝑥 ∈ V ↦ {𝑦𝑦 (𝑥 ∩ 𝒫 𝑦)})
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-topgen
StepHypRef Expression
1 ctg 15869 . 2 class topGen
2 vx . . 3 setvar 𝑥
3 cvv 3172 . . 3 class V
4 vy . . . . . 6 setvar 𝑦
54cv 1473 . . . . 5 class 𝑦
62cv 1473 . . . . . . 7 class 𝑥
75cpw 4107 . . . . . . 7 class 𝒫 𝑦
86, 7cin 3538 . . . . . 6 class (𝑥 ∩ 𝒫 𝑦)
98cuni 4366 . . . . 5 class (𝑥 ∩ 𝒫 𝑦)
105, 9wss 3539 . . . 4 wff 𝑦 (𝑥 ∩ 𝒫 𝑦)
1110, 4cab 2595 . . 3 class {𝑦𝑦 (𝑥 ∩ 𝒫 𝑦)}
122, 3, 11cmpt 4637 . 2 class (𝑥 ∈ V ↦ {𝑦𝑦 (𝑥 ∩ 𝒫 𝑦)})
131, 12wceq 1474 1 wff topGen = (𝑥 ∈ V ↦ {𝑦𝑦 (𝑥 ∩ 𝒫 𝑦)})
Colors of variables: wff setvar class
This definition is referenced by:  tgval  20517
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