Generalized cell maps

In [6] the notion of a g-cell structure was introduced as a generalization of the construction proposed by Debski and Tymchatyn to realize a certain class of topological spaces as quotient spaces of inverse limits. In [2], cell maps are defined between cell structures and showed that a cell map between two complete cell structures induces a continuous function between the spaces determined by the cell structures. In this paper, for g-cell structures, we introduce the notions of weak g-cell maps and g-cell maps. We give some conditions for weak g-cell and g-cell mappings between g-cell structures to induce continuous mappings between their corresponding spaces.