Another Approach to Topological Descent Theory

In the category Top of topological spaces and continuous functions we prove that descent morphisms with respect to the class IE of continuous bijections are exactly the descent mor phisms providing a new characterization of the latter in terms of sub brations IE X of the basic bration given by Top X which are essentially complete lattices Also e ective descent morphisms are characterized in terms of e ective morphisms with respect to continuous bijec tions For classes IE satisfying suitable conditions we show that the class of e ective descent morphisms coincides with the one of e ective IE descent morphisms