Definition df-ii 24392

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 ∘ − ) ↾ ((0[,]1) × (0[,]1))))

Detailed syntax breakdown of Definition df-ii

Step	Hyp	Ref	Expression
1		cii 24390	. 2 class II
2		cabs 15180	. . . . 5 class abs
3		cmin 11443	. . . . 5 class −
4	2, 3	ccom 5680	. . . 4 class (abs ∘ − )
5		cc0 11109	. . . . . 6 class 0
6		c1 11110	. . . . . 6 class 1
7		cicc 13326	. . . . . 6 class [,]
8	5, 6, 7	co 7408	. . . . 5 class (0[,]1)
9	8, 8	cxp 5674	. . . 4 class ((0[,]1) × (0[,]1))
10	4, 9	cres 5678	. . 3 class ((abs ∘ − ) ↾ ((0[,]1) × (0[,]1)))
11		cmopn 20933	. . 3 class MetOpen
12	10, 11	cfv 6543	. 2 class (MetOpen‘((abs ∘ − ) ↾ ((0[,]1) × (0[,]1))))
13	1, 12	wceq 1541	1 wff II = (MetOpen‘((abs ∘ − ) ↾ ((0[,]1) × (0[,]1))))

This definition is referenced by:  iitopon  24394  dfii2  24397  dfii3  24398  lebnumii  24481