Axiomatic shape theory
HTML articles powered by AMS MathViewer
- by Philip Bacon
- Proc. Amer. Math. Soc. 53 (1975), 489-496
- DOI: https://doi.org/10.1090/S0002-9939-1975-0420611-2
- PDF | Request permission
Abstract:
The notion of shape theory is so defined that, if ${\text {H}}$ is a category and ${\text {W}}$ is a subcategory of ${\text {H}}$, all shape theories on $({\text {H,}}\;{\text {W}})$ are isomorphic and, under a mild condition, a shape theory on $({\text {H,}}\;{\text {W}})$ always exists. Additional theorems facilitate the comparison of shape theories constructed by various means.References
- Karol Borsuk, Concerning homotopy properties of compacta, Fund. Math. 62 (1968), 223–254. MR 229237, DOI 10.4064/fm-62-3-223-254
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
- Ralph H. Fox, On shape, Fund. Math. 74 (1972), no. 1, 47–71. MR 296914, DOI 10.4064/fm-74-1-47-71
- Horst Herrlich and George E. Strecker, Category theory: an introduction, Allyn and Bacon Series in Advanced Mathematics, Allyn and Bacon, Inc., Boston, Mass., 1973. MR 0349791
- W. Holsztyński, An extension and axiomatic characterization of Borsuk’s theory of shape, Fund. Math. 70 (1971), no. 2, 157–168. MR 282368, DOI 10.4064/fm-70-2-157-168
- Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 0181977
- G. Kozlowski and J. Segal, On the shape of $0$-dimensional paracompacta, Fund. Math. 83 (1974), no. 2, 151–154. MR 334142, DOI 10.4064/fm-83-2-151-154
- Sibe Mardešić, Shapes for topological spaces, General Topology and Appl. 3 (1973), 265–282. MR 324638
- Sibe Mardešić and Jack Segal, Shapes of compacta and ANR-systems, Fund. Math. 72 (1971), no. 1, 41–59. MR 298634, DOI 10.4064/fm-72-1-41-59
- E. Michael, A short proof of the Arens-Eells embedding theorem, Proc. Amer. Math. Soc. 15 (1964), 415–416. MR 162222, DOI 10.1090/S0002-9939-1964-0162222-5
- T. Porter, Generalised shape theory, Proc. Roy. Irish Acad. Sect. A 74 (1974), 33–48. MR 367915
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 489-496
- MSC: Primary 55D99
- DOI: https://doi.org/10.1090/S0002-9939-1975-0420611-2
- MathSciNet review: 0420611