In this paper, a number of novel properties of reactor network synthesis (RNS) problems are presented and proved within the Infinite DimEnsionAl State-space (IDEAS) framework for isothermal reactor networks with and without the constant density assumption. These properties can then be used to reduce the dimension of the composition space (i.e., concentration space for constant density fluid (CDF) reactor networks, mass fraction space for variable density fluid (VDF) reactor networks) within which RNS is conducted and subsequently the attainable region (AR) construction. This procedure may be used to overcome the difficulty preventing the AR methodology and other RNS methods from being used for real industrial size problems. (C) 2007 Published by Elsevier Ltd.