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Definition df-topsp 12104
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
StepHypRef Expression
1 ctps 12103 . 2 class TopSp
2 vf . . . . . 6 setvar 𝑓
32cv 1313 . . . . 5 class 𝑓
4 ctopn 12027 . . . . 5 class TopOpen
53, 4cfv 5091 . . . 4 class (TopOpen‘𝑓)
6 cbs 11865 . . . . . 6 class Base
73, 6cfv 5091 . . . . 5 class (Base‘𝑓)
8 ctopon 12083 . . . . 5 class TopOn
97, 8cfv 5091 . . . 4 class (TopOn‘(Base‘𝑓))
105, 9wcel 1463 . . 3 wff (TopOpen‘𝑓) ∈ (TopOn‘(Base‘𝑓))
1110, 2cab 2101 . 2 class {𝑓 ∣ (TopOpen‘𝑓) ∈ (TopOn‘(Base‘𝑓))}
121, 11wceq 1314 1 wff TopSp = {𝑓 ∣ (TopOpen‘𝑓) ∈ (TopOn‘(Base‘𝑓))}
Colors of variables: wff set class
This definition is referenced by:  istps  12105
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