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a-discrete a-r-discrete analogous belongs choose Clearly closed image closed mapping closed sets cofinal coinitial collectionwise normal Consequently consists of convex contained convex open neighbourhood convex sets COROLLARY countable E-network countably compact cX is metrizable define denoted E-space elements of F(n endgap F e F F e F(n finite-to-one G.-diagonal GO-space hence homeomorphic implies interior gaps ISBN 90 left endpoint left neighbour left right left-isolated lemma let f Let U(n lexicographic product Lindelof linearly ordered set locally finite LOTS LUTZER M-space Math metrizable space Moore space Moreover Nagata space natural number open covers open image open mapping open set order preserving order topology ordered spaces paracompact p-space PROOF proposition 1.2.3 proposition 2.1.1 prove pseudogap quasi-perfect map quotient space right endpoint right-isolated semi-metrizable sequence of open sequence x(n Sorgenfrey line St(x subspace suppose topological space x e F y e cX