ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-topon GIF version

Definition df-topon 12215
Description: Define the function that associates with a set the set of topologies on it. (Contributed by Stefan O'Rear, 31-Jan-2015.)
Assertion
Ref Expression
df-topon TopOn = (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = 𝑗})
Distinct variable group:   𝑗,𝑏

Detailed syntax breakdown of Definition df-topon
StepHypRef Expression
1 ctopon 12214 . 2 class TopOn
2 vb . . 3 setvar 𝑏
3 cvv 2689 . . 3 class V
42cv 1331 . . . . 5 class 𝑏
5 vj . . . . . . 7 setvar 𝑗
65cv 1331 . . . . . 6 class 𝑗
76cuni 3743 . . . . 5 class 𝑗
84, 7wceq 1332 . . . 4 wff 𝑏 = 𝑗
9 ctop 12201 . . . 4 class Top
108, 5, 9crab 2421 . . 3 class {𝑗 ∈ Top ∣ 𝑏 = 𝑗}
112, 3, 10cmpt 3996 . 2 class (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = 𝑗})
121, 11wceq 1332 1 wff TopOn = (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = 𝑗})
Colors of variables: wff set class
This definition is referenced by:  funtopon  12216  istopon  12217  toponsspwpwg  12226  dmtopon  12227
  Copyright terms: Public domain W3C validator