Discrete cells properties in the boundary set setting

Author:
Philip L. Bowers

Journal:
Proc. Amer. Math. Soc. **93** (1985), 735-740

MSC:
Primary 57N20

MathSciNet review:
776212

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the complement of a -set in a locally compact separable ANR. It is proved that satisfies the discrete -cells property for each nonnegative integer if and only if satisfies the discrete approximation property. As a consequence, Hilbert space manifolds that arise as complements of boundary sets in Hilbert cube manifolds are characterized in terms of their homological structure coupled with a minimal amount of general positioning.

**[BBMW]**Mladen Bestvina, Philip Bowers, Jerzy Mogilski, and John Walsh,*Characterization of Hilbert space manifolds revisited*, Topology Appl.**24**(1986), no. 1-3, 53–69. Special volume in honor of R. H. Bing (1914–1986). MR**872478**, 10.1016/0166-8641(86)90049-0**[Bol]**P. L. Bowers,*Applications of general position properties of dendrites to Hilbert space topology*, Ph.D. Diss., Univ. of Tennessee, 1983.**[Bo2]**-,*Dense embeddings of sigma-compact, nowhere locally compact metric spaces*, preprint.**[Cu]**D. W. Curtis,*Boundary sets in the Hilbert cube*, Topology Appl.**20**(1985), no. 3, 201–221. MR**804034**, 10.1016/0166-8641(85)90089-6**[DW]**Robert J. Daverman and John J. Walsh,*Čech homology characterizations of infinite-dimensional manifolds*, Amer. J. Math.**103**(1981), no. 3, 411–435. MR**618319**, 10.2307/2374099**[To1]**H. Toruńczyk,*On 𝐶𝐸-images of the Hilbert cube and characterization of 𝑄-manifolds*, Fund. Math.**106**(1980), no. 1, 31–40. MR**585543****[To2]**H. Toruńczyk,*Characterizing Hilbert space topology*, Fund. Math.**111**(1981), no. 3, 247–262. MR**611763**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1985-0776212-6

Keywords:
Discrete approximation property,
discrete -cells property

Article copyright:
© Copyright 1985
American Mathematical Society