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1. CMB 1997 (vol 40 pp. 395)
| $D$-spaces and resolution A space $X$ is a $D$-space if, for every neighborhood assignment $f$
there is a closed discrete set $D$ such that $\bigcup{f(D)}=X$. In this
paper we give some necessary conditions and some sufficient conditions
for a resolution of a topological space to be a $D$-space. In particular,
if a space $X$ is resolved at each $x\in X$ into a $D$-space $Y_x$ by
continuous mappings $f_x\colon X-\{{x}\} \rightarrow Y_x$, then the
resolution is a $D$-space if and only if $\bigcup{\{{x}\}}\times \Bd(Y_x)$
is a $D$-space.
Keywords:$D$-space, neighborhood assignment, resolution, boundary Categories:54D20, 54B99, 54D10, 54D30 |

