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.