Alonso Morón, ManuelRomero Ruiz Del Portal, Francisco2023-06-202023-06-201999-04-14Alonso Morón, M., Romero Ruiz Del Portal, F. «On Weak Shape Equivalences». Topology and Its Applications, vol. 92, n.o 3, abril de 1999, pp. 225-36. DOI.org (Crossref), https://doi.org/10.1016/S0166-8641(97)00252-6.0166-864110.1016/S0166-8641(97)00252-6https://hdl.handle.net/20.500.14352/57320We prove that weak shape equivalences are monomorphisms in the shape category of uniformly pointed movable continua Sh(M). We use an example of Draper and Keesling to show that weak shape equivalences need not be monomorphisms in the shape category. We deduce that Sh(M) is not balanced. We give a characterization of weak dominations in the shape category of pointed continua, in the sense of Dydak (1979). We introduce the class of pointed movable triples (X,F,Y), for a shape morphism F:X --> Y, and we establish an infinite-dimensional Whitehead theorem in shape theory from which we obtain, as a corollary, that for every pointed movable pair of continua (Y,X) the embedding j: X --> Y is a shape equivalence iff it is a weak shape equivalence.engjournal articlehttps//doi.org/10.1016/S0166-8641(97)00252-6http://www.sciencedirect.com/science/article/pii/S0166864197002526open access515.143HomotopyMonomorphismsEpimorphismsWeak shape equivalenceShape category of uniformly pointed movable continuaMonomorphisms and epimorphisms in categoriesTopología1210 Topología