One-to-one mappings
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- by Dix H. Pettey PDF
- Proc. Amer. Math. Soc. 31 (1972), 276-278 Request permission
Abstract:
In an earlier paper, the author showed that ${E^2}$ can never be the image, under a nontopological $1 - 1$ mapping, of a connected, locally connected, locally compact topological space. In this paper, we show that several other spaces, including ${S^2}$ and ${I^2}$ share this property with ${E^2}$.References
- Dix H. Pettey, Mappings onto the plane, Trans. Amer. Math. Soc. 157 (1971), 297–309. MR 275395, DOI 10.1090/S0002-9947-1971-0275395-9
- V. V. Proisvolov, One-to-one mappings onto metric spaces, Dokl. Akad. Nauk SSSR 158 (1964), 788–789 (Russian). MR 0175091 W. Sierpiński, Sur les espaces métriques localement séparables, Fund. Math. 21 (1933), 107-113.
- Gordon Thomas Whyburn, Analytic topology, American Mathematical Society Colloquium Publications, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1963. MR 0182943
- G. T. Whyburn, On compactness of mappings, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1426–1431. MR 176450, DOI 10.1073/pnas.52.6.1426
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 276-278
- DOI: https://doi.org/10.1090/S0002-9939-1972-0288735-8
- MathSciNet review: 0288735