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1. CMB 2010 (vol 53 pp. 360)
Separating H-sets by Open Sets In an H-closed, Urysohn space, disjoint H-sets can be separated by disjoint open sets. This is not true for an arbitrary H-closed space even if one of the H-sets is a point. In this paper, we provide a systematic study of those spaces in which disjoint H-sets can be separated by disjoint open sets.
Keywords:H-set, H-closed, θ-continuous Categories:54C08, 54D10, 54D15 |
2. 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 |
3. CMB 1997 (vol 40 pp. 39)
On projective $Z$-frames This paper deals with the projective objects in the category of all
$Z$-frames, where the latter is a common generalization of
different types of frames. The main result obtained here is that a
$Z$-frame is ${\bf E}$-projective if and only if it is stably
$Z$-continuous, for a naturally arising collection ${\bf E}$ of morphisms.
Categories:06D05, 54D10, 18D15 |