Suppose that Va aA is a collection of nonempty open sets in Rn which satisfies Va V for all in A Prove that A is countable What happens to this result when open is omitted

Question: Suppose that {Va}aA is a collection of nonempty open sets in Rn which satisfies Va V = for all in

Suppose that {Va}a∈A is a collection of nonempty open sets in Rn which satisfies Va ∩ Vβ = θ for all α ≠ β in A. Prove that A is countable. What happens to this result when open is omitted?

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