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Definition df-topgen 12157
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. (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 12151 . 2 class topGen
2 vx . . 3 setvar 𝑥
3 cvv 2686 . . 3 class V
4 vy . . . . . 6 setvar 𝑦
54cv 1330 . . . . 5 class 𝑦
62cv 1330 . . . . . . 7 class 𝑥
75cpw 3510 . . . . . . 7 class 𝒫 𝑦
86, 7cin 3070 . . . . . 6 class (𝑥 ∩ 𝒫 𝑦)
98cuni 3736 . . . . 5 class (𝑥 ∩ 𝒫 𝑦)
105, 9wss 3071 . . . 4 wff 𝑦 (𝑥 ∩ 𝒫 𝑦)
1110, 4cab 2125 . . 3 class {𝑦𝑦 (𝑥 ∩ 𝒫 𝑦)}
122, 3, 11cmpt 3989 . 2 class (𝑥 ∈ V ↦ {𝑦𝑦 (𝑥 ∩ 𝒫 𝑦)})
131, 12wceq 1331 1 wff topGen = (𝑥 ∈ V ↦ {𝑦𝑦 (𝑥 ∩ 𝒫 𝑦)})
Colors of variables: wff set class
This definition is referenced by:  tgval  12234  eltg4i  12240  eltg3  12242  tg1  12244  tg2  12245  tgclb  12250
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