▁ ▁Sem if inals ▁ ▁Bron ze ▁medal ▁game ▁ ▁Final ▁ ▁Final ▁stand ings ▁ ▁External ▁links ▁Official ▁Website ▁ ▁References ▁ ▁Baseball ▁at ▁the ▁Central ▁American ▁and ▁Car ib bean ▁Games ▁Category : Events ▁at ▁the ▁ 2 0 1 0 ▁Central ▁American ▁and ▁Car ib bean ▁Games ▁ 2 0 1 0 ▁ 2 0 1 0 <0x0A> </s> ▁In ▁mathematics , ▁a ▁finite ▁topological ▁space ▁is ▁a ▁topological ▁space ▁for ▁which ▁the ▁underlying ▁point ▁set ▁is ▁finite . ▁That ▁is , ▁it ▁is ▁a ▁topological ▁space ▁for ▁which ▁there ▁are ▁only ▁finit ely ▁many ▁points . ▁ ▁While ▁topology ▁has ▁mainly ▁been ▁developed ▁for ▁infinite ▁spaces , ▁finite ▁topological ▁spaces ▁are ▁often ▁used ▁to ▁provide ▁examples ▁of ▁interesting ▁phen omena ▁or ▁counter examples ▁to ▁pla us ible ▁sound ing ▁conject ures . ▁William ▁Th ur ston ▁has ▁called ▁the ▁study ▁of ▁finite ▁top ologies ▁in ▁this ▁sense ▁" an ▁odd ball ▁topic ▁that ▁can ▁l end ▁good ▁insight ▁to ▁a ▁variety ▁of ▁questions ". ▁ ▁Top ologies ▁on ▁a ▁finite ▁set ▁ ▁As ▁a ▁bounded ▁sub l attice ▁ ▁A ▁topology ▁on ▁a ▁set ▁X ▁is ▁defined ▁as ▁a ▁subset ▁of ▁P ( X ), ▁the ▁power ▁set ▁of ▁X , ▁which ▁includes ▁both ▁ ∅ ▁and ▁X ▁and ▁is ▁closed ▁under ▁finite ▁inter sections ▁and ▁arbitrary ▁un ions . ▁ ▁Since ▁the ▁power ▁set ▁of ▁a ▁finite ▁set ▁is ▁finite ▁there ▁can ▁be ▁only ▁finit ely ▁many ▁open ▁sets ▁( and ▁only ▁finit ely ▁many ▁closed ▁sets ).