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Intrinsic topologies in topological lattices and semilattices

1973
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Pacific Journal of Mathematics
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{L(x):xeL} and all sets {M{x):xeL}. If L does not have universal bounds, then a set K c L is closed if K Π [a, b] is closed in the interval topology of the sublattice [α, b] for all a, b with a ^ 6. (2) The order topology (0). A net {x a } in L is said to orderconverge to # if there exist a monotonic ascending net {t a } with a;sup t a (t a t a?) and a monotonic descending net {u a } with a? = inf u a {u a \ x) such that for all α, ί β ^ # α ^ w β . A subset A of L is ciosβd in the order

doi:10.2140/pjm.1973.44.593
fatcat:xaxdeohngja7xhi67l6uaxyccm