Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

$ {\rm UV}$ properties of compact sets


Author: Steve Armentrout
Journal: Trans. Amer. Math. Soc. 143 (1969), 487-498
MSC: Primary 54.55; Secondary 55.00
DOI: https://doi.org/10.1090/S0002-9947-1969-0273573-7
MathSciNet review: 0273573
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] W. R. Alford and R. B. Sher, A note on 0-dimensional decompositions of $ {E^3}$, Amer. Math. Monthly 75 (1968), 337-378. MR 0226615 (37:2204)
  • [2] -, Decompositions of $ {E^3}$ with a compact 0-dimensional set of nondegenerate elements, Trans. Amer. Math. Soc. 123 (1966), 165-177. MR 0195074 (33:3279)
  • [3] -, Concerning cellular decompositions of 3-manifolds that yield 3-manifolds, Trans. Amer. Math. Soc. 133 (1968), 307-332. MR 0230296 (37:5859)
  • [4] -, Cellular decompositions of 3-manifolds that yield 3-manifolds, Bull. Amer. Math. Soc. 75 (1969), 453-455. MR 0239578 (39:935)
  • [5] -, On the strong local simple connectivity of the decomposition spaces of toroidal decomposition, (to appear).
  • [6] -, Small compact simply connected neighborhoods in certain decomposition spaces, (to appear).
  • [7] W. R. Alford and R. B. Sher., A property of a decomposition space described by Bing, Notices Amer. Math. Soc. 11 (1964), 369-370.
  • [8] -, Homotopy properties of decomposition spaces, Trans. Amer. Math. Soc. 143 (1969), 499-507. MR 0273574 (42:8452)
  • [9] S. Armentrout and T. M. Price, Decompositions into compact sets with UV properties, Trans. Amer. Math. Soc. MR 0244994 (39:6307)
  • [10] S. Armentrout, L. L. Lininger and D. V. Meyer, Equivalent decompositions of $ {E^3}$, Pacific J. Math. 24 (1968), 205-227. MR 0224070 (36:7117)
  • [11] E. Artin and R. H. Fox, Some wild cells and spheres in three dimensional space, Ann. of Math. 49 (1948), 979-990. MR 0027512 (10:317g)
  • [12] R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653-663. MR 0043450 (13:265a)
  • [13] -, Necessary and sufficient conditions that a 3-manifold be $ {S^3}$, Ann. of Math. 68 (1958), 17-37. MR 0095471 (20:1973)
  • [14] K. Borsuk, Theory of retracts, Monogr. Mat., Vol. 44, Polish Scientific Publisher, Warsaw, 1967. MR 0216473 (35:7306)
  • [15] D. M. Hyman, ANR divisors and absolute neighborhood contractibility, Fund. Math. 62 (1968), 61-73. MR 0229197 (37:4771)
  • [16] R. C. Lacher, Cell-like spaces and mappings, Bull. Amer. Math. Soc. 74 (1968), 933-935. MR 0244963 (39:6276)
  • [17] J. Martin, The sum of two crumpled cubes, Michigan Math. J. 13 (1966), 147-151. MR 0190914 (32:8324)
  • [18] D. R. McMillan, Jr., A criterion for cellularity in a manifold, Ann. of Math. 79 (1964), 327-337. MR 0161320 (28:4528)
  • [19] T. M. Price, Upper semi-continuous decompositions of $ {E^3}$, Thesis, University of Wisconsin, Madison, 1964.
  • [20] -, A necessary condition that a cellular upper semicontinuous decomposition of $ {E^n}$ yield $ {E^n}$, Trans. Amer. Math. Soc. 122 (1966), 427-435. MR 0193627 (33:1843)
  • [21] S. Smale, A Vietoris mapping theorem for homotopy, Proc. Amer. Math. Soc. 8 (1957), 604-610. MR 0087106 (19:302f)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54.55, 55.00

Retrieve articles in all journals with MSC: 54.55, 55.00


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1969-0273573-7
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society