The
semi-
wD
spaces are
defined in terms of semi-open covers and they generalize simultaneously the wD
spaces and the
semi-developable spaces. We prove the following results in this paper:
·
A topological space is a semi-wD
space if and
only if it is a q-space and a b-space.
·
The semi-wD
property is
invariant under continuous, finite to one, pseudo-open maps.
·
An isocompact semi-wD
space with a
semi-
property
is q-refinable.
·
A topological space is semi-metrizable if and only if it is a semi-developable
space with a quasi
-diagonal.
·
A topological space is a Hausdorff semi-metrizable space if and only if it is a
semi-wD
space with an
-diagonal.
·
A topological space is a regular semi-metrizable space if and only
if it is a semi-wD space with a semi-
property
and a quasi
-diagonal.
The
following results are corollaries of the main results about the semi- wD spaces:
·
A topological space is a Moore space if and only if it is a wD-space with a semi-
property
and a quasi
-diagonal.
·
A regular topological space is a Moore space if and only if it is a wD-space with an
-diagonal.
·
A topological space is a metrizable space if and only if it is a wM
space with a semi-
property
and a quasi
-diagonal.
· A topological space is a metrizable space if and only if it is a wM
space with an
-diagonal.
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