  The research of attribute characters in information system which contains
core, necessary, unnecessary is a basic and important issue in attribute
reduct. Many methods for the judgement of attribute characters are based on the
relationship between the objects and attributes. In this paper, a new type of
judgement theorems which are absolutely based on the relationship among
attributes is proposed for the judgement of attribute characters. The method is
through comparing the two new attribute sets $E(a)$ and $N(a)$ with respect to
the designated attribute $a$ which is proposed in this paper. We conclude that
which type of the attribute $a$ belongs to is determined by the relationship
between $E(a)$ and $N(a)$ in essence. Secondly, more concise and clear results
are given about the judgment of the attribute characters through analyzing the
properties of refinement and precise-refinement between $E(a)$ and $N(a)$ in
topology. In addition, the relationship among attributes are discussed which is
useful for constructing a reduct in the last section of this paper. In the
last, we propose a reduct algorithm based on $E(a)$, and this algorithm is an
extended application of the analysis of attribute characters above.
