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Keywords:
$D$-space; sequential space; $wcs^*$-network; weakly monotonically monolithic space
$D$-space; sequential space; $wcs^*$-network; weakly monotonically monolithic space
Summary:
In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a $D$-space. Thus most known conclusions on $D$-spaces can be obtained by this conclusion. As a corollary, we have that if a regular space $X$ is sequential and has a point-countable $wcs^*$-network then $X$ is a $D$-space.
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