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One of the main notions in the Rough Sets Theory (RST) is that of a reduct. According to its classic definition, the reduct is a minimal subset of the attributes that retains some important properties of the whole set of attributes. The idea of the reduct proved to be interesting enough to inspire a great deal of research and resulted in introducing various reduct-related ideas and notions. First of all, depending on the character of the attributes involved in the analysis, so called absolute and relative reducts can be defined. The more interesting of these, relative reducts, are minimal subsets of attributes that retain discernibility between objects belonging to different classes. This paper focuses on the topological aspects of such reducts, identifying some of their limitations and introducing alternative definitions that do not suffer from these limitations. The modified subsets of attributes, referred to as constructs, are intended to …