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Definition df-tvc 23060
Description: Define a topological left vector space, which is a topological module over a topological division ring. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
df-tvc TopVec = {𝑤 ∈ TopMod ∣ (Scalar‘𝑤) ∈ TopDRing}

Detailed syntax breakdown of Definition df-tvc
StepHypRef Expression
1 ctvc 23056 . 2 class TopVec
2 vw . . . . . 6 setvar 𝑤
32cv 1542 . . . . 5 class 𝑤
4 csca 16805 . . . . 5 class Scalar
53, 4cfv 6380 . . . 4 class (Scalar‘𝑤)
6 ctdrg 23054 . . . 4 class TopDRing
75, 6wcel 2110 . . 3 wff (Scalar‘𝑤) ∈ TopDRing
8 ctlm 23055 . . 3 class TopMod
97, 2, 8crab 3065 . 2 class {𝑤 ∈ TopMod ∣ (Scalar‘𝑤) ∈ TopDRing}
101, 9wceq 1543 1 wff TopVec = {𝑤 ∈ TopMod ∣ (Scalar‘𝑤) ∈ TopDRing}
Colors of variables: wff setvar class
This definition is referenced by:  istvc  23089
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