feat: prove T313, hyperconnected implies the countable chain condition - #1335
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feat: prove T313, hyperconnected implies the countable chain condition#1335kisonecat wants to merge 1 commit into
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T313: a hyperconnected space satisfies the countable chain condition.A hyperconnected space has no two disjoint nonempty open sets at all, so a pairwise disjoint
family of open sets has at most one nonempty member. Such a family is contained in
insert ∅ {one set}, hence countable — the bound is far stronger than countability.Closes #567.