Laguna, V. F.Rodríguez Sanjurjo, José Manuel2023-06-212023-06-211984S. Bogatyi, Approximate and fundamental retracts, Mat. Sbornik 93 (135) (1974) 90-102. (Math. USSR Sbornik 22 (1974) 91-103). K. Borsuk, Theory of Shape, (Monografie Matematycne 59, Polish Scientific Publishers, Warszawa 1975). K. Borsuk, On a class of compacta, Houston J. IMath. 1 (1975) 1-13. L. Boxer, Maps related to calmness, Topology Appl. 15 (1983) 11-17. Z. Cerin, Surjective approximate absolute (neighborhood) retracts, Topology Proceedings 6 (1981) 5-27. Z. Cerin, VP-e-movable and O-e-calm compacta and their images, Compositio klath. 45 (1981) 115-141. Z. Cerin, ANR’s and AANR’s revisited, A talk presented at the Conference on Shape Theory and Geometric Topology, Dubrovnik, Yugoslavia, 1981. M.H. Clapp, On a generalization of absolute neighborhood retracts, Fund. Math. 70 (1971) 117-l 30. J. Dydak, On internally movable compacta, Bull. Acad. Polon. Sci. 27 (1979) 107-l 10. J. Dydak and J. Segal, Shape theory: An introduction, (Lecture Notes in .Math. 688, Springer, Berlin 1978). J. Dydak and J. Segal, Approximate Polyhedra and Shape Theory, Topology Proceedings 6 ( 198 1). A. Grnurczyk, Approximate retracts and fundamental retracts. Colloq. Math. 23 (1971) 61-63. A. Granas. Fixed point theorems for the approximative ANR’s, Bull. Acad. Polon. Sci. 16 (1968) 15-19. S.T. Hu, Theory of Retracts (Wayne State Univ. Press. Detroit, 1965). S. MardeGL On Borsuk’s shape theory for compact pairs, Bull. Acad. Polon. Sci. 21 (1973) 1131-1136. S. MardeSif, Approximate polyhedra. resolutions of maps and shape fibrations, Fund. Math. 114 (1981) 53-78. S. MardeSiC and J. Segal, Shape Theory (North-Holland, Amsterdam, 1982). H. Noguchi, A generalization of absolute neighborhood retracts, Kodai Math. Sem. Reports 1 (1953) X-22. P. Patten, Refinable maps and generalized absolute neighborhood retracts, Topology Appl. 14 (1982) 183-188. S. Spiei, Movability and uniform movability, Bull. Acad. Polon. Sci. 22 (1974) 43-45. T. Watanabe. Approximative Shape Theory, to appear.0166-864110.1016/0166-8641(84)90041-5https://hdl.handle.net/20.500.14352/64694We introduce the notion of internal fundamental sequence and prove that any shape morphism from an arbitrary compactum X to an internally movable compactum Y is induced by an internal fundamental sequence. We use this special kind of fundamental sequences to give characterizations and some properties of AANRc-sets and AANR,-sets. The paper ends with a section devoted to internal FANR’s.engjournal articlehttp://www.sciencedirect.com/science/article/pii/0166864184900415http://www.sciencedirect.com/restricted access514515.1Shape theoryGeometríaTopología1204 Geometría1210 Topología