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Definition df-topn 13322
Description: Define the topology extractor function. This differs from df-tset 13221 when a structure has been restricted using df-ress 13149; in this case the TopSet component will still have a topology over the larger set, and this function fixes this by restricting the topology as well. (Contributed by Mario Carneiro, 13-Aug-2015.)
Assertion
Ref Expression
df-topn  |-  TopOpen  =  ( w  e.  _V  |->  ( (TopSet `  w )t  ( Base `  w ) ) )

Detailed syntax breakdown of Definition df-topn
StepHypRef Expression
1 ctopn 13320 . 2  class  TopOpen
2 vw . . 3  set  w
3 cvv 2789 . . 3  class  _V
42cv 1623 . . . . 5  class  w
5 cts 13208 . . . . 5  class TopSet
64, 5cfv 5221 . . . 4  class  (TopSet `  w )
7 cbs 13142 . . . . 5  class  Base
84, 7cfv 5221 . . . 4  class  ( Base `  w )
9 crest 13319 . . . 4  classt
106, 8, 9co 5819 . . 3  class  ( (TopSet `  w )t  ( Base `  w
) )
112, 3, 10cmpt 4078 . 2  class  ( w  e.  _V  |->  ( (TopSet `  w )t  ( Base `  w
) ) )
121, 11wceq 1624 1  wff  TopOpen  =  ( w  e.  _V  |->  ( (TopSet `  w )t  ( Base `  w ) ) )
Colors of variables: wff set class
This definition is referenced by:  topnfn  13324  topnval  13333
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