Subbases, Convex Sets, and Hyperspaces
نویسندگان
چکیده
S[ and Sg are then said to separate (or: to screen) S± and S2. Finally, Sf is called a binary subbase if each linked system S^ (zS^ (i.e., a subcollection S^' of ^ of which any two members meet) satisfies ς\Sf'φ 0. It is well-known that a binary subbase is TΊ (cf. van Mill [9, Lemma 1]), that a space carrying a binary subbase is compact (use Alexander's lemma), and that a space is completely regular iff it admits a normal Tλ (sub)base (cf. Frink [6, Thm. 1]; de Groot and Aarts [1, Thm. 2]).
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