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Definition df-utop 19941
Description: Definition of a topology induced by a uniform structure. Definition 3 of [BourbakiTop1] p. II.4. (Contributed by Thierry Arnoux, 17-Nov-2017.)
Assertion
Ref Expression
df-utop  |- unifTop  =  ( u  e.  U. ran UnifOn  |->  { a  e.  ~P dom  U. u  |  A. x  e.  a  E. v  e.  u  ( v " { x } ) 
C_  a } )
Distinct variable group:    u, a, v, x

Detailed syntax breakdown of Definition df-utop
StepHypRef Expression
1 cutop 19940 . 2  class unifTop
2 vu . . 3  setvar  u
3 cust 19909 . . . . 5  class UnifOn
43crn 4952 . . . 4  class  ran UnifOn
54cuni 4202 . . 3  class  U. ran UnifOn
6 vv . . . . . . . . 9  setvar  v
76cv 1369 . . . . . . . 8  class  v
8 vx . . . . . . . . . 10  setvar  x
98cv 1369 . . . . . . . . 9  class  x
109csn 3988 . . . . . . . 8  class  { x }
117, 10cima 4954 . . . . . . 7  class  ( v
" { x }
)
12 va . . . . . . . 8  setvar  a
1312cv 1369 . . . . . . 7  class  a
1411, 13wss 3439 . . . . . 6  wff  ( v
" { x }
)  C_  a
152cv 1369 . . . . . 6  class  u
1614, 6, 15wrex 2800 . . . . 5  wff  E. v  e.  u  ( v " { x } ) 
C_  a
1716, 8, 13wral 2799 . . . 4  wff  A. x  e.  a  E. v  e.  u  ( v " { x } ) 
C_  a
1815cuni 4202 . . . . . 6  class  U. u
1918cdm 4951 . . . . 5  class  dom  U. u
2019cpw 3971 . . . 4  class  ~P dom  U. u
2117, 12, 20crab 2803 . . 3  class  { a  e.  ~P dom  U. u  |  A. x  e.  a  E. v  e.  u  ( v " { x } ) 
C_  a }
222, 5, 21cmpt 4461 . 2  class  ( u  e.  U. ran UnifOn  |->  { a  e.  ~P dom  U. u  |  A. x  e.  a  E. v  e.  u  ( v " { x } ) 
C_  a } )
231, 22wceq 1370 1  wff unifTop  =  ( u  e.  U. ran UnifOn  |->  { a  e.  ~P dom  U. u  |  A. x  e.  a  E. v  e.  u  ( v " { x } ) 
C_  a } )
Colors of variables: wff setvar class
This definition is referenced by:  utopval  19942
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