A cellular map between nonhomeomorphic polyhedra whose nondegeneracy set is a null sequence

Henderson, James P.

doi:10.1090/S0002-9939-1982-0656121-0

A cellular map between nonhomeomorphic polyhedra whose nondegeneracy set is a null sequence
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Proc. Amer. Math. Soc. 85 (1982), 447-450 Request permission

Abstract:

A cellular map between nonhomeomorphic polyhedra whose nondegeneracy set consists of a null sequence of cellular sets is constructed. The construction begins with Daverman’s example of a cellular map between nonhomeomorphic polyhedra and uses an amalgamation technique.

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
M. A. Armstrong, Transversality for polyhedra, Ann. of Math. (2) 86 (1967), 172–191. MR 219075, DOI 10.2307/1970365
R. H. Bing, Point-like decompositions of $E^{3}$, Fund. Math. 50 (1961/62), 431–453. MR 137104, DOI 10.4064/fm-50-4-431-453
Robert J. Daverman, A nonshrinkable decomposition of $S^{n}$ determined by a null sequence of cellular sets, Proc. Amer. Math. Soc. 75 (1979), no. 1, 171–176. MR 529236, DOI 10.1090/S0002-9939-1979-0529236-5

Approximating certain cell-like maps by homeomorphisms

James P. Henderson, Cellularity in polyhedra, Topology Appl. 12 (1981), no. 3, 267–282. MR 623735, DOI 10.1016/0166-8641(81)90005-5
James P. Henderson, Approximating cellular maps between low-dimensional polyhedra, Pacific J. Math. 101 (1982), no. 2, 321–331. MR 675404
James P. Henderson, Cellular maps between polyhedra, Trans. Amer. Math. Soc. 272 (1982), no. 2, 527–537. MR 662050, DOI 10.1090/S0002-9947-1982-0662050-3
C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972. MR 0350744
L. C. Siebenmann, Approximating cellular maps by homeomorphisms, Topology 11 (1972), 271–294. MR 295365, DOI 10.1016/0040-9383(72)90014-6
John J. Walsh, Isotoping mappings to open mappings, Trans. Amer. Math. Soc. 250 (1979), 121–145. MR 530046, DOI 10.1090/S0002-9947-1979-0530046-8
David G. Wright, A decomposition of $E^{n}$ $(n\geq 3)$ into points and a null sequence of cellular sets, General Topology Appl. 10 (1979), no. 3, 297–304. MR 546103