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...Solutionstoexercisesfor mathematicsa part fall ii metric and topological spaces closed sets limit points problems from munkres pp show that if a is in y x then solution since we can write f where an intersection fo set it follows also let b determine whether the following inclusions hold equality fails deter mine containment one way or other holds c implies which yields inclusion to see may be proper take open intervals real line left hand side empty but right this time shall rst give example properly contains second now always given need for eacn u containing nonempty such condition hence boundary bd dened by expression int are disjoint their union closure of interior complement while contained latter so only both therefore means must reverses roles preceding two sentences denition thus equal its own reduces on know sincebothsummandsofthelefthandsidearecontainedinx d true justify your answer no as subset r however have because footnote property described called regular find each subse...