Some special decompositions of $E^{3}$
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- by Charles D. Bass
- Trans. Amer. Math. Soc. 216 (1976), 115-130
- DOI: https://doi.org/10.1090/S0002-9947-1976-0405425-7
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Abstract:
A great deal of attention has been given to the question: which upper semicontinuous decompositions of ${E^3}$ into pointlike continua give ${E^3}$. It has recently been determined that some decompositions of ${E^3}$ into points and straight line segments give decomposition spaces which are topologically distinct from ${E^3}$. In this paper we apply a new condition to the set of nondegenerate elements of a decomposition which enables one to conclude that the resulting decomposition space is homeomorphic to ${E^3}$.References
- Steve Armentrout, Cellular decompositions of $3$-manifolds that yield $3$-manifolds, Memoirs of the American Mathematical Society, No. 107, American Mathematical Society, Providence, R.I., 1971. MR 0413104
- R. H. Bing, Upper semicontinuous decompositions of $E^3$, Ann. of Math. (2) 65 (1957), 363β374. MR 92960, DOI 10.2307/1969968 β, Decompositions of ${E^3}$, Topology of 3-manifolds and related topics (Proc. the Univ. of Georgia Institute, 1961), Prentice-Hall, Englewood Cliffs, N. J., 1962, pp. 5-21. MR 25 #4501.
- E. Dyer and M.-E. Hamstrom, Completely regular mappings, Fund. Math. 45 (1958), 103β118. MR 92959, DOI 10.4064/fm-45-1-103-118
- W. T. Eaton, Applications of a mismatch theorem to decomposition spaces, Fund. Math. 89 (1975), no.Β 3, 199β224. MR 391095, DOI 10.4064/fm-89-3-199-224
- Louis F. McAuley, Some upper semi-continuous decompositions of $E^{3}$ into $E^{3}$, Ann. of Math. (2) 73 (1961), 437β457. MR 126258, DOI 10.2307/1970312 β, Upper semicontinuous decompositions of ${E^3}$ into ${E^3}$ and generalizations to metric spaces, Topology of 3-manifolds and related topics (Proc. the Univ. of Georgia Institute, 1961), Prentice-Hall, Englewood Cliffs, N. J., 1962, pp. 21-26. MR 25 #4502.
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 216 (1976), 115-130
- MSC: Primary 57A10; Secondary 54B15
- DOI: https://doi.org/10.1090/S0002-9947-1976-0405425-7
- MathSciNet review: 0405425