Abstract view
$D$spaces and resolution


Published:19971201
Printed: Dec 1997
Abstract
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.
MSC Classifications: 
54D20, 54B99, 54D10, 54D30 show english descriptions
Noncompact covering properties (paracompact, Lindelof, etc.) None of the above, but in this section Lower separation axioms ($T_0$$T_3$, etc.) Compactness
54D20  Noncompact covering properties (paracompact, Lindelof, etc.) 54B99  None of the above, but in this section 54D10  Lower separation axioms ($T_0$$T_3$, etc.) 54D30  Compactness
