Q4. Let E be an Archimedean Riesz space, A ⊆ ℝ bounded above. Then show that supremum of the set

Name: Q4. Let E be an Archimedean Riesz space, A ⊆ ℝ bounded above. Then show that supremum of the set Ax = {α x : α∈ A} exists and sup(Ax) = (sup A)x
Uploaded: 2023-01-17T01:35:00-08:00
Duration: 4 min 20 s
Channel: Oswaldo Jiménez
Description: Q4. Let E be an Archimedean Riesz space, A ⊆ ℝ bounded above. Then show that supremum of the set Ax = {α x : α∈ A} exists and sup(Ax) = (sup A)x

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Oswaldo Jiménez · Accepted Answer

Step 1: Since E is an Archimedean Riesz space, it satisfies the Archimedean property, which stat

Question

Q4. Let E be an Archimedean Riesz space, A \(\subseteq\) \(\mathbb{R}\) bounded above. Then show that supremum of the set \(Ax = \{\alpha x : \alpha \in A\}\) exists and \(\sup(Ax) = (\sup A)x\)

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