THE ω-REGULAR SEPERATION AXIOM IN Lω-SPACES

The concepts of ω-regular and ωT3 separation axioms are introduced in Lω-spaces. The characterizations of ω-regular and ωT3 separation are systematically discussed. Seven equivalent conditions of ω-regular separation are given. That ω-regular and ωT3 separations are hereditary, arbitrary multiplicative under condition of full-stratum, topological invariant under (ω1 ,ω2)-homeomorphic order-homomorphism and the good extension in the sense of R. Lowen, are proved.