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Classes in which Open Sets are Defined PACE 1 Open sets
Interior and exterior elements The frontier of a set The border of a set
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aggregate of sets analytical set belongs to F Borel sets bounded sets cardinal closed and compact closed set compact set continued fraction continuous and biuniform continuous transform continuum Corollary countable aggregate countable set countable subset deduced defined definition denote a given dense-in-itself derived set different elements easily seen element of condensation element p0 exists an element exists an infinite exists an open finite number follows at once Frechet function f(p given element given set Hence Hilbert space homeomorphic hypothesis infinite sequence irrational numbers lemma Let p denote limit element metric space mutually exclusive sets natural numbers necessary and sufficient non-countable nucleus null set obtained obviously open set containing ordinal number positive integer potency Proof proved rational numbers rational set real numbers sequence p„(n set Gs set Q sets belonging Suppose Theorem 39 topological space transfinite induction