✦ LIBER ✦

Closure Algebras and Boolean Algebras

✍ Scribed by G. J. Logan

Publisher: John Wiley and Sons
Year: 1977
Tongue: English
Weight: 212 KB
Volume: 23
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19770230107

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✦ Synopsis

S(z A y ) z S(A), by (c) * S(z) A S(Y) 2 S(A) e S(x) 2 S(A) and S(y) 2 S(A) e C ( s ) s C ( A ) 'and C ( y ) E C ( A ) , by (c) o x € C ( A ) and Y E C ( A ) .

Now every ultrafilter is consistent and closed with respect to C, since if U is an ultrafilter and C ( U ) = X , then C({,uu,, . . ., ,u,&}) = X for some pl, . . ., pn E U by the cocompactness of ( X , C ) . Hence S({pl, . . ., pn)) = 0 so that n S(pJ = 0, and

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