Geodesic
On weakly monotonically monolithic spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 133-142

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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.
Classification : 54F99, 54G99
Keywords: $D$-space; sequential space; $wcs^*$-network; weakly monotonically monolithic space 
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Peng, Liang-Xue. On weakly monotonically monolithic spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 133-142. http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a10/