Definition df-topsp 12823

Description: Define the class of topological spaces (as extensible structures). (Contributed by Stefan O'Rear, 13-Aug-2015.)

Assertion

Ref	Expression
df-topsp	⊢ TopSp = {𝑓 ∣ (TopOpen‘𝑓) ∈ (TopOn‘(Base‘𝑓))}

Detailed syntax breakdown of Definition df-topsp

Step	Hyp	Ref	Expression
1		ctps 12822	. 2 class TopSp
2		vf	. . . . . 6 setvar 𝑓
3	2	cv 1347	. . . . 5 class 𝑓
4		ctopn 12580	. . . . 5 class TopOpen
5	3, 4	cfv 5198	. . . 4 class (TopOpen‘𝑓)
6		cbs 12416	. . . . . 6 class Base
7	3, 6	cfv 5198	. . . . 5 class (Base‘𝑓)
8		ctopon 12802	. . . . 5 class TopOn
9	7, 8	cfv 5198	. . . 4 class (TopOn‘(Base‘𝑓))
10	5, 9	wcel 2141	. . 3 wff (TopOpen‘𝑓) ∈ (TopOn‘(Base‘𝑓))
11	10, 2	cab 2156	. 2 class {𝑓 ∣ (TopOpen‘𝑓) ∈ (TopOn‘(Base‘𝑓))}
12	1, 11	wceq 1348	1 wff TopSp = {𝑓 ∣ (TopOpen‘𝑓) ∈ (TopOn‘(Base‘𝑓))}

This definition is referenced by:  istps  12824