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Definition df-ii 17082
Description: Define the unit interval with the Euclidean topology. (Contributed by Jeff Madsen, 2-Sep-2009.) (Revised by Mario Carneiro, 3-Sep-2015.)
Assertion
Ref Expression
df-ii  |-  II  =  ( MetOpen `  ( ( abs  o.  -  )  |`  ( ( 0 [,] 1 )  X.  (
0 [,] 1 ) ) ) )

Detailed syntax breakdown of Definition df-ii
StepHypRef Expression
1 cii 17080 . 2  class  II
2 cabs 10929 . . . . 5  class  abs
3 cmin 8458 . . . . 5  class  -
42, 3ccom 4266 . . . 4  class  ( abs 
o.  -  )
5 cc0 8164 . . . . . 6  class  0
6 c1 8165 . . . . . 6  class  1
7 cicc 10042 . . . . . 6  class  [,]
85, 6, 7co 5366 . . . . 5  class  ( 0 [,] 1 )
98, 8cxp 4260 . . . 4  class  ( ( 0 [,] 1 )  X.  ( 0 [,] 1 ) )
104, 9cres 4264 . . 3  class  ( ( abs  o.  -  )  |`  ( ( 0 [,] 1 )  X.  (
0 [,] 1 ) ) )
11 cmopn 15096 . . 3  class  MetOpen
1210, 11cfv 4274 . 2  class  ( MetOpen `  ( ( abs  o.  -  )  |`  ( ( 0 [,] 1 )  X.  ( 0 [,] 1 ) ) ) )
131, 12wceq 1520 1  wff  II  =  ( MetOpen `  ( ( abs  o.  -  )  |`  ( ( 0 [,] 1 )  X.  (
0 [,] 1 ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  iitopon  17084  dfii2  17087  dfii3  17088  lebnumii  17163
Copyright terms: Public domain