Definition df-ii 22488

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 22486	. 2 class II
2		cabs 13822	. . . . 5 class abs
3		cmin 10145	. . . . 5 class −
4	2, 3	ccom 5042	. . . 4 class (abs ∘ − )
5		cc0 9815	. . . . . 6 class 0
6		c1 9816	. . . . . 6 class 1
7		cicc 12049	. . . . . 6 class [,]
8	5, 6, 7	co 6549	. . . . 5 class (0[,]1)
9	8, 8	cxp 5036	. . . 4 class ((0[,]1) × (0[,]1))
10	4, 9	cres 5040	. . 3 class ((abs ∘ − ) ↾ ((0[,]1) × (0[,]1)))
11		cmopn 19557	. . 3 class MetOpen
12	10, 11	cfv 5804	. 2 class (MetOpen‘((abs ∘ − ) ↾ ((0[,]1) × (0[,]1))))
13	1, 12	wceq 1475	1 wff II = (MetOpen‘((abs ∘ − ) ↾ ((0[,]1) × (0[,]1))))

This definition is referenced by:  iitopon  22490  dfii2  22493  dfii3  22494  lebnumii  22573