## The Dror-Whitehead theorem in prohomotopy and shape theories

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- by S. Singh PDF
- Trans. Amer. Math. Soc.
**268**(1981), 487-496 Request permission

## Abstract:

Many analogues of the classical Whitehead theorem from homotopy theory are now available in pro-homotopy and shape theories. E. Dror has significantly extended the homology version of the Whitehead theorem from the well-known simply connected case to the more general, for instance, nilpotent case. We prove a full analogue of Drorâs theorems in pro-homotopy and shape theories. More specifically, suppose $\underline f :\underline X \to \underline Y$ is a morphism in the pro-homotopy category of pointed and connected topological spaces which induces isomorphisms of the integral homology pro-groups. Then $\underline f$ induces isomorphisms of the homotopy pro-groups, for instance, when $\underline X$ and $\underline Y$ are simple, nilpotent, complete, or $\underline H$-objects; these notions are well known in homotopy theory and we have naturally extended them to pro-homotopy and shape theories.## References

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## Additional Information

- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**268**(1981), 487-496 - MSC: Primary 55P10; Secondary 55P55
- DOI: https://doi.org/10.1090/S0002-9947-1981-0632540-7
- MathSciNet review: 632540