The closed disks touch at (1,0), so their connected union M is connected. Their open interiors are disjoint, nonempty open components and separate N. Thus **C**.
More Connectedness and Compactness questions
GATE 2022 MA Q22– Let T₁ be the usual subspace topology on [0,1] and T₂ any topology there. P:if T₁⊊T₂, then…
GATE 2022 MA Q24– Give Y=∏ₙ₌₁∞ℝ its product topology and Δ=(x,x,x,…):x∈ℝ its subspace topology. Which holds?
GATE 2021 MA Q52– Let X₁ be ℝ with upper-limit basis (a,b], and X₂ be ℝ with the cofinite topology. Which…
GATE 2026 MA Q24– Give ℝ the cofinite topology =\A R:Ac is finite\\\. Which statements hold?
GATE 2026 MA Q45– For subsets E₁,E₂ of a normed space, define E₁+E₂ = x+y:x∈E₁,y∈E₂ and E₁×E₂ as their…
GATE 2026 MA Q49– S= n=1\(x,y) R2:(x-n)2+y2=1/n2\ with the usual topology. Which statements hold?