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Definition df-mopn 12186
Description: Define a function whose value is the family of open sets of a metric space. (Contributed by NM, 1-Sep-2006.)
Assertion
Ref Expression
df-mopn MetOpen = (𝑑 ran ∞Met ↦ (topGen‘ran (ball‘𝑑)))

Detailed syntax breakdown of Definition df-mopn
StepHypRef Expression
1 cmopn 12180 . 2 class MetOpen
2 vd . . 3 setvar 𝑑
3 cxmet 12175 . . . . 5 class ∞Met
43crn 4543 . . . 4 class ran ∞Met
54cuni 3739 . . 3 class ran ∞Met
62cv 1330 . . . . . 6 class 𝑑
7 cbl 12177 . . . . . 6 class ball
86, 7cfv 5126 . . . . 5 class (ball‘𝑑)
98crn 4543 . . . 4 class ran (ball‘𝑑)
10 ctg 12161 . . . 4 class topGen
119, 10cfv 5126 . . 3 class (topGen‘ran (ball‘𝑑))
122, 5, 11cmpt 3992 . 2 class (𝑑 ran ∞Met ↦ (topGen‘ran (ball‘𝑑)))
131, 12wceq 1331 1 wff MetOpen = (𝑑 ran ∞Met ↦ (topGen‘ran (ball‘𝑑)))
Colors of variables: wff set class
This definition is referenced by:  mopnrel  12636  mopnval  12637  isxms2  12647
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