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Definition df-mopn 16371
Description: Define a function whose value is the family of open sets of a metric space. See elmopn 17983 for its main property. (Contributed by NM, 1-Sep-2006.)
Assertion
Ref Expression
df-mopn  |-  MetOpen  =  ( d  e.  U. ran  * Met  |->  ( topGen `  ran  ( ball `  d )
) )

Detailed syntax breakdown of Definition df-mopn
StepHypRef Expression
1 cmopn 16367 . 2  class  MetOpen
2 vd . . 3  set  d
3 cxmt 16364 . . . . 5  class  * Met
43crn 4690 . . . 4  class  ran  * Met
54cuni 3829 . . 3  class  U. ran  * Met
62cv 1623 . . . . . 6  class  d
7 cbl 16366 . . . . . 6  class  ball
86, 7cfv 5222 . . . . 5  class  ( ball `  d )
98crn 4690 . . . 4  class  ran  ( ball `  d )
10 ctg 13337 . . . 4  class  topGen
119, 10cfv 5222 . . 3  class  ( topGen ` 
ran  ( ball `  d
) )
122, 5, 11cmpt 4079 . 2  class  ( d  e.  U. ran  * Met  |->  ( topGen `  ran  ( ball `  d )
) )
131, 12wceq 1624 1  wff  MetOpen  =  ( d  e.  U. ran  * Met  |->  ( topGen `  ran  ( ball `  d )
) )
Colors of variables: wff set class
This definition is referenced by:  mopnval  17979  isxms2  17989  setsmstopn  18019  tngtopn  18161
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