Using results of EscardóFlagg [1] and Hofmann [2], we characterize continuous maps which are injective with respect to special classes of embeddings. These characterizations are based on a fibrewise waybelow relation which generalizes the one used by Richter in his characterization of fibrewise exponentiability [3]. (Joint work with Francesca Cagliari and Sandra Mantovani.) References: [1] M. Escardó, R. Flagg, Semantic domains, injective spaces and monads, Electr. Notes in Theor. Comp. Science 20, electronic paper 15 (1999). [2] D. Hofmann, A four for the price of one duality principle for distributive topological spaces, preprint, arXiv:math.GN/1102.2605. [3] G. Richter, Exponentiability for maps means fibrewise corecompactness, J. Pure Appl. Algebra 187 (2004), 295303.
