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Definition df-tgp 17772
Description: Define the class of all topological groups. A topological group is a group whose operation and inverse function are continuous. (Contributed by FL, 18-Apr-2010.)
Assertion
Ref Expression
df-tgp  |-  TopGrp  =  {
f  e.  ( Grp 
i^i TopMnd )  |  [. ( TopOpen
`  f )  / 
j ]. ( inv g `  f )  e.  ( j  Cn  j ) }
Distinct variable group:    f, j

Detailed syntax breakdown of Definition df-tgp
StepHypRef Expression
1 ctgp 17770 . 2  class  TopGrp
2 vf . . . . . . 7  set  f
32cv 1631 . . . . . 6  class  f
4 cminusg 14379 . . . . . 6  class  inv g
53, 4cfv 5271 . . . . 5  class  ( inv g `  f )
6 vj . . . . . . 7  set  j
76cv 1631 . . . . . 6  class  j
8 ccn 16970 . . . . . 6  class  Cn
97, 7, 8co 5874 . . . . 5  class  ( j  Cn  j )
105, 9wcel 1696 . . . 4  wff  ( inv g `  f )  e.  ( j  Cn  j )
11 ctopn 13342 . . . . 5  class  TopOpen
123, 11cfv 5271 . . . 4  class  ( TopOpen `  f )
1310, 6, 12wsbc 3004 . . 3  wff  [. ( TopOpen
`  f )  / 
j ]. ( inv g `  f )  e.  ( j  Cn  j )
14 cgrp 14378 . . . 4  class  Grp
15 ctmd 17769 . . . 4  class TopMnd
1614, 15cin 3164 . . 3  class  ( Grp 
i^i TopMnd )
1713, 2, 16crab 2560 . 2  class  { f  e.  ( Grp  i^i TopMnd )  |  [. ( TopOpen `  f )  /  j ]. ( inv g `  f )  e.  ( j  Cn  j ) }
181, 17wceq 1632 1  wff  TopGrp  =  {
f  e.  ( Grp 
i^i TopMnd )  |  [. ( TopOpen
`  f )  / 
j ]. ( inv g `  f )  e.  ( j  Cn  j ) }
Colors of variables: wff set class
This definition is referenced by:  istgp  17776
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