Let X = {a, b, c, d} and Y = {x, Y, z, w} be two topological spaces with topologies Ti = {X,0, {a}, {a, b}, {a, b, c}} T2 = {Y, 0, {x}, {y}, {x, y}, {y, z, w}}, respectively. Consider the functions f: X → Y and g : X → Y defined by the and diagrams below: 00 00 a a b. b d d Determine which function is continuous and which is not. Show your solution.

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