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Note on Attaching Dold Fibrations

Published online by Cambridge University Press:  20 November 2018

Philip R. Heath  and
Klaus Heiner Kamps
Philip R. Heath
Affiliation:
Department of Mathematics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada. A1B 3X7
Klaus Heiner Kamps
Affiliation:
Fachbereich Mathematik, Eernunrversitat, Postfach 940, D-5800 Hagen
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In this note, we patch up the proof of a Theorem due to Handel on the characterization of homotopy epimorphisms ([6], 2.2) and generalize a Theorem due to Ibisch on attaching disk-bundles to Dold fibrations ([7], Satz 1).

We work throughout in the category TopB of spaces over B for some fixed topological space B.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 3 , 01 September 1978 , pp. 365 - 367
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Arnold, J. E. Jr, Attaching Hurewicz fibrations with fiber preserving maps. Pacific J. Math. 46, 325-335 (1973).Google Scholar
2. Dieck, T. tom, Partitions of unity in homotopy theory. Compositio Math. 23,159-167 (1971).Google Scholar
3. Dieck, T.tom, Kamps, K. H., Puppe, D., Homotopietheoie. Lecture Notes in Mathematics 157, Berlin-Heidelberg-New York: Springer, 1970.Google Scholar
4. Dold, A., Partitions of unity in the theory of fibrations. Ann. of Math, 78, 223-255 (1963).Google Scholar
5. Dold, A., Die Homotopieerweiterungseïgenschaft ( = HEP) ist eine lokale Eigenschaft. Inventiones Math. 6, 185-189 (1968).Google Scholar
6. Handel, D., Epimorphism plus monomorphism implies equivalence in the homotopy category. J. Pure Appl. Algebra 6, 357-360 (1975).Google Scholar
7. Ibisch, H. D., Anheften von Kugelbündeln an Faserräume. Math. Z. 91, 294-299 (1966).Google Scholar
8. James, I. M., Overhomotopy theory. Symposia Mathematica 4, 219-229 (1970).Google Scholar
9. Kamps, K. H., Kan-Bedingungen und abstrakte Homotopietheorie. Math. Z. 124, 215-236 (1972).Google Scholar
10. Spanier, E. H., Algebraic Topology, New York: McGraw-Hill, 1966.Google Scholar
11. Strøm, A., Note on cofibrations. Math. Scand. 19.11-14 (1966).Google Scholar