The map x↦(x,x,…) is a homeomorphism from ℝ to Δ, with inverse the first-coordinate projection. Thus Δ is connected and locally compact. A cylinder restricting the first two coordinates to disjoint intervals misses Δ, so it is not dense. Any basic neighborhood restricts only finitely many coordinates and allows a point off Δ, so Δ is not open. **B**.
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