Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: D-completion, well-filterification and sobrification   In this paper, we obtain some sufficient conditions for the D-completion of a
T0 space to be the well-filterification of this space, the well-filterification
of a T0 space to be the sobrification of this space and the D-completion of a
T0 space to be the sobrification, respectively. Moreover, we give an example to
show that a tapered closed set may be neither the closure of a directed set nor
the closed KF-set, respectively. Because the tapered closed set is a closed
WD-set, the example also gives a negative answer to a problem proposed by Xu.
Meantime, a new direct characterization of the D-completion of a T0 space is
given by using the notion of pre-c-compact elements.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci