Let (X, T1) and (Y, T2) be topological spaces. Show that the set {U × Y ∣ U ∈ T1} ∪ {X × V ∣ V ∈ T2} is a subbasis for the product topology of X × Y..

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Q: 43. Choose the number q so that (if possible) the ranks are (a) 1, (b) 2, (c) 3: 6 4 2 -3 -2 -1 9 6…

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Q: prove v(x1) = v(xn) → x1 injective if x1 ‡xn → v(x1) ‡ v(xn) v →x1 = xn ⇒

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Q: if the radius of a circle is increased by 3, the circumference is increased by how much?

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Q: Let be unique equilibrium of the equation (1), then ♫ 1+ N.N.N.N.N.N Ω= ⇒ ² = 0 ⇒ = 0, So, = 0…

A: Given: The nonlinear difference equation, Ωm+1=Ωm-7q+61+∏t=05Ωm-q+1t-q, m=0,1,...   To prove: Ω¯=0,…

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