We investigate the existence of injective hulls (with respect to the class of embeddings) in the categories Top_o/B$ of T_o topological fibre spaces over B. We prove that, if f:A----> B has a restriction to the image injective in Top_o/f(A), (A,f) has an injective hull in Top_o/B$ if and only if f(A') is locally closed in B, where A' denotes the union of non-indiscrete fibres of f.
Injective hulls of $T\sb 0$ topological fibre spaces / F. Cagliari, S. Mantovani. - In: APPLIED CATEGORICAL STRUCTURES. - ISSN 0927-2852. - 11:4(2003), pp. 377-390.
Injective hulls of $T\sb 0$ topological fibre spaces
S. MantovaniUltimo
2003
Abstract
We investigate the existence of injective hulls (with respect to the class of embeddings) in the categories Top_o/B$ of T_o topological fibre spaces over B. We prove that, if f:A----> B has a restriction to the image injective in Top_o/f(A), (A,f) has an injective hull in Top_o/B$ if and only if f(A') is locally closed in B, where A' denotes the union of non-indiscrete fibres of f.
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