Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-18T13:44:46.978Z Has data issue: false hasContentIssue false

On a Kind of Homotopy Manifold

Published online by Cambridge University Press:  20 November 2018

T. Akasaki*
Affiliation:
Rutgers—The State University, New Brunswick, New Jersey
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In a recent paper (6), S. T. Hu investigated the initial projection from the mth enveloping space of a topological space X into X and proved that, under some local conditions on X, the initial projection is a fibering. In a subsequent paper (7), Hu showed that the terminal projection from the mth enveloping space is a fibering without assuming the local conditions on X and in (8) he used the terminal projection from the second enveloping space in his topological immersion theorem.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Curtis, M. L., Homotopically homogeneous polyhedra, Michigan Math. J., 8 (1963), 5560.Google Scholar
2. Curtis, M. L., Homotopy manifolds, Topology of 3-manifolds (Englewood Cliffs, N.J., 1962), 102104.Google Scholar
3. Fadell, E., A note on the non-existence of strongly homogeneous, AR's, Bull. Acad. Polon. Sci. Ser., 12 (1964), 531534.Google Scholar
4. Hu, S. T., Homotopy theory (New York, 1959).Google Scholar
5. Hu, S. T., Isotopy invariants of topological spaces, Proc. Roy. Soc. (London), Ser. A, 255 (1960), 331366.Google Scholar
6. Hu, S. T., Fiberings of enveloping spaces, I, Proc. London Math. Soc., Ser. III, 11 (1961), 691707.Google Scholar
7. Hu, S. T., Fiberings of enveloping spaces, II, Tôhoku Math. J., 14 (1962), 104120.Google Scholar
8. Hu, S. T., Immersions of compact metric spaces into euclidean spaces, Illinois Math. J., 7 (1963), 415424.Google Scholar
9. Hu, S. T., Elements of general topology (San Francisco, 1964).Google Scholar
10. Kosiński, A., On manifolds and r-spaces, Fund. Math., 42 (1955), 111124.Google Scholar
11. Raymond, F., Local triviality for Hurewicz fiberings of manifolds, Topology 3 (1965), 4357.Google Scholar