Definition df-hmeo 12475

Description: Function returning all the homeomorphisms from topology j to topology k. (Contributed by FL, 14-Feb-2007.)

Assertion

Ref	Expression
df-hmeo	|- Homeo = ( j e. Top , k e. Top |-> { f e. ( j Cn k ) | `' f e. ( k Cn j ) } )

Distinct variable group:   f, j, k

Detailed syntax breakdown of Definition df-hmeo

Step	Hyp	Ref	Expression
1		chmeo 12474	. 2 class Homeo
2		vj	. . 3 setvar j
3		vk	. . 3 setvar k
4		ctop 12169	. . 3 class Top
5		vf	. . . . . . 7 setvar f
6	5	cv 1330	. . . . . 6 class f
7	6	ccnv 4538	. . . . 5 class `' f
8	3	cv 1330	. . . . . 6 class k
9	2	cv 1330	. . . . . 6 class j
10		ccn 12359	. . . . . 6 class Cn
11	8, 9, 10	co 5774	. . . . 5 class ( k Cn j )
12	7, 11	wcel 1480	. . . 4 wff `' f e. ( k Cn j )
13	9, 8, 10	co 5774	. . . 4 class ( j Cn k )
14	12, 5, 13	crab 2420	. . 3 class { f e. ( j Cn k ) | `' f e. ( k Cn j ) }
15	2, 3, 4, 4, 14	cmpo 5776	. 2 class ( j e. Top , k e. Top |-> { f e. ( j Cn k ) | `' f e. ( k Cn j ) } )
16	1, 15	wceq 1331	1 wff Homeo = ( j e. Top , k e. Top |-> { f e. ( j Cn k ) | `' f e. ( k Cn j ) } )

This definition is referenced by:  hmeofn  12476  hmeofvalg  12477  ishmeo  12478