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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  e.  _V  |->  { j  e.  Top  | 
b  =  U. 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  U. j
84, 7wceq 1332 . . . 4  wff  b  = 
U. j
9 ctop 12201 . . . 4  class  Top
108, 5, 9crab 2421 . . 3  class  { j  e.  Top  |  b  =  U. j }
112, 3, 10cmpt 3996 . 2  class  ( b  e.  _V  |->  { j  e.  Top  |  b  =  U. j } )
121, 11wceq 1332 1  wff TopOn  =  ( b  e.  _V  |->  { j  e.  Top  | 
b  =  U. j } )
Colors of variables: wff set class
This definition is referenced by:  funtopon  12216  istopon  12217  toponsspwpwg  12226  dmtopon  12227
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