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0] iff distinct points of X have disjoint vg-closures.
1] then distinct points of X have disjoint vg-closures.
Thus G and X - U are disjoint vg-open sets containing x and y respectively.
1] can be expressed as a disjoint union of a class C of countably infinite sets, the cardinality of C being [[omega].
40, a set X being infinite, it can be expressed as a disjoint union of a class C of countably infinite sets that is, each of which has cardinality [omega].
alpha]] are pairwise disjoint and there is a bijection [f.
Then C and Fr(O) are disjoint closed sets and by Urysohn's lemma, there exists a continuous function f: (X,T) [right arrow]([0, 1],S) such that f(C) = 0 and f(Fr(O)) = 1.
5, 1]) are disjoint open sets containing C and Fr(O), respectively.
When the 1988 study was conducted, the two literatures on migraine and on magnesium were essentially disjoint in that they had virtually no articles or authors in common, they did not cite each other, and they were not cited together (cocited) by any third type of article (a few exceptions are discussed in that study; no subsequent publications have yet identified other pre-1988 exceptions, and even the exceptions have not been cited).
A "literature intervention" is here taken to be a published literature analysis or bibliometric analysis that attempts to introduce new connections and citations that cut across specialties in order to connect disjoint parts of the existing network.
n] y of X there exists disjoint v--open sets G and H such that G containing x but not y and H containing y but not x.
2], there exist disjoint v--open sets U and V in X such that x [member of] U, y [not member of] U and y [member of] V, x [not member of] V.