The standard metric on R is d: R? → [0, 0) defined by d(x, y) = |x – yl. a. Show that the resulting basis for the standard topology on R consists of all intervals (a, b) where a < b. b. Write down three open subsets of R that are not of the form (a, b).

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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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