Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: d-independence and d-bases in vector lattices   This article contains the results of two types. First we give a complete
characterization of band preserving projection operators on Dedekind complete
vector lattices. This is done in Theorem~3.4. Let us mention also Theorem~3.2
that contains a description of such operators on arbitrary laterally complete
vector lattices. The central role in these descriptions is played by d-bases,
one of two principal tools utilized in our work [{\it Inverses of Disjointness
Preserving Operators}, Memoirs of the Amer. Math. Soc., forthcoming]. The
concept of a d-basis has been applied so far only to vector lattices with a
large amount of projection bands. The absence of the projection bands has been
the major obstacle for extending, otherwise very useful concept of d-bases, to
arbitrary vector lattices. In Section~4 we overcome this obstacle by finding a
new way to introduce d-independence in an arbitrary vector lattice. This allows
us to produce a new definition of a d-basis which is free of the existence of
projection bands. We illustrate this by proving several results devoted to
cardinality of d-bases. Theorems~4.13 and~4.15 are the main of them and they
assert that, under very general conditions, a vector lattice either has a
singleton d-basis of else this d-basis must be infinite.

21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex