Consider the set of mathematical formulas F, Inductively defined as the smallest set that meets the following rules: 1. VNEN, nEF 2. Yes F1, F2 E F, then: · Fr. F2 EF · F1 - F2 EF · F: F2 EF · Fu F2 EF c) Prove VFE FIt is true that # op ( F) S#n( F). Hint: Can you find an equality that relates both values?

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A: This is a problem of Real topology, metric topology.

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Q: Let E be a set that bounded and c > 0. Prove that sup(cE) = -c inf(-E)

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