Characterizations of K-semimetric spaces

Abstract EN

In this paper, we prove, for a space X, the following are equivalent : 1.

X is a ω Δ1 space with a regular-G δ-diagonal, 2.

X is a ω Δ2 space with a regular-G δ-diagonal, 3.

X is a semi-developable space with G δ- (3) –diagonal, 4.

X is a ω Δ1-space with a G δ (3)-diagonal, 5.

X is a ω Δ2-space with a G δ (3)-diagonal, 6.

X is a q, β -space with a G* δ (2)-diagonal, 7.

X is a semi-developable space with G* δ (2)-diagonal, 8.

X is a semimetrizable, c-stratifiable space, 9.

X is a c-Nagata β –space, 10.

X is a K-semimetrizable.