By B. Banaschewski (auth.), Horst Herrlich, Gerhard Preuß (eds.)
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Additional info for Categorical Topology: Proceedings of the International Conference, Berlin, August 27th to September 2nd, 1978
Sample text
Is a set m a p ~({x}) f >(Y,B,4) = x is g i v e n set-theoretical and forgetful reflective completion. triples and (X,A,~) is c o n t a i n e d is the are all of f ~(M) functor MacNeille : ~(f[M]) (with completion, 21 Main ideas of the reflective the proof: MacNeille non-existence a class class class KC L the property EK has smallest not 8EL \ K . L contain Hence, > e EL of <{I},P> we d e f i n e e, and p~ W we give 1¢ a concrete set-indexed any > of <{l},P> we h a v e class if M = {~}, O, if M = W \M) ~K ~ ~K' collection (b).
And M. Jerison. Nostrand, Princeton-New Rings of continuous York, 1960. M. T0-separation Math. 2(1977), 177-190. -E. (E,M)-universally topological tationssehrift, Univ. D~sseldorf, 1974. C. Bitopological (1963),71-89. P. Bitopological spaces and quasi-uniform London Math. Soc. (3)17(1967),241-256. G. Bibliography on quasi-uniform spaces. , Univ. of Alberta, Edmonton, 1974. [18] Nachbin, L. Sur les espaces uniformes Paris 226(1948), 774-775. J. Pairwise complete regularity and eompactification in bitopological spaces.
We is t h e X. quotient quotient class of the space [7]. i[A] space Now c ~X as u s u a l projection. all continuous to E a n d topology by X(A). by "x ~ y iff x h a s natural initial claim is Y and Denote Identify belonging with way. is a T 1 - s p a c e A of be the spaces a T1-space relation Then which closed. following subset ) ~X/i[A] set ~ X / i [ A ] s u p p l i e d to C ( ~ X / i [ A ] ) . A. with o corresponding Furthermore to be to is a R - s p a c e is not equivalence j: X X(A) there in the as y").