A manifold localcompactification of a metric combinatorial manifold
Author:
Katsuro Sakai
Journal:
Proc. Amer. Math. Soc. 100 (1987), 775780
MSC:
Primary 57N20; Secondary 54E45, 54F40, 57Q15
MathSciNet review:
894453
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Abstract: Let be a combinatorial manifold, that is, a countable simplicial complex such that the star of each vertex is combinatorially equivalent to the countableinfinite full simplicial complex. Then the space with the metric topology is a manifold modeled on the space , where is the subspace of the Hilbert cube which consists of all points having at most finitely many nonzero coordinates. In this paper, we give a localcompactification of which is a stable manifold containing as an f.d. cap set.
 [An]
R. D. Anderson, On sigmacompact subsets of infinitedimensional spaces, unpublished manuscript.
 [Ch]
T.
A. Chapman, Dense sigmacompact subsets of
infinitedimensional manifolds, Trans. Amer.
Math. Soc. 154
(1971), 399–426. MR 0283828
(44 #1058), http://dx.doi.org/10.1090/S00029947197102838287
 [Ch]
T.
A. Chapman, On the structure of Hilbert cube manifolds,
Compositio Math. 24 (1972), 329–353. MR 0305432
(46 #4562)
 [CDM]
Doug
Curtis, Tadeusz
Dobrowolski, and Jerzy
Mogilski, Some applications of the topological
characterizations of the sigmacompact spaces 𝑙²_{𝑓}
and Σ, Trans. Amer. Math. Soc.
284 (1984), no. 2,
837–846. MR
743748 (86i:54035), http://dx.doi.org/10.1090/S00029947198407437487
 [Du]
J.
Dugundji, Locally equiconnected spaces and absolute
neighborhood, Fund. Math. 57 (1965), 187–193.
MR
0184202 (32 #1675)
 [Hu]
Szetsen
Hu, Theory of retracts, Wayne State University Press, Detroit,
1965. MR
0181977 (31 #6202)
 [Ke]
OttHeinrich
Keller, Die Homoiomorphie der kompakten konvexen Mengen im
Hilbertschen Raum, Math. Ann. 105 (1931), no. 1,
748–758 (German). MR
1512740, http://dx.doi.org/10.1007/BF01455844
 [Mo]
Jerzy
Mogilski, Characterizing the topology of
infinitedimensional 𝜎compact manifolds, Proc. Amer. Math. Soc. 92 (1984), no. 1, 111–118. MR 749902
(85m:57012), http://dx.doi.org/10.1090/S00029939198407499028
 [Sa]
K. Sakai, Combinatorial infinitedimensional manifolds and manifolds, Topology Appl. (to appear).
 [Sa]
Katsuro
Sakai, On topologies of triangulated infinitedimensional
manifolds, J. Math. Soc. Japan 39 (1987), no. 2,
287–300. MR
879930 (88e:57020), http://dx.doi.org/10.2969/jmsj/03920287
 [Sa]
, Simplicial complexes triangulating infinitedimensional manifolds, preprint.
 [Sa]
, Completions of metric simplicial complexes by using norms, preprint.
 [To]
H.
Toruńczyk, On 𝐶𝐸images of the Hilbert cube
and characterization of 𝑄manifolds, Fund. Math.
106 (1980), no. 1, 31–40. MR 585543
(83g:57006)
 [Wo]
R. Y.T. Wong, Noncompact Hilbert cube manifolds, unpublished manuscript.
 [An]
 R. D. Anderson, On sigmacompact subsets of infinitedimensional spaces, unpublished manuscript.
 [Ch]
 T. A. Chapman, Dense sigmacompact subsets of infinitedimensional manifolds, Trans. Amer. Math. Soc. 154 (1971), 399426. MR 0283828 (44:1058)
 [Ch]
 , On the structure of Hilbert cube manifolds, Compositio Math. 24 (1972), 329353. MR 0305432 (46:4562)
 [CDM]
 D. W. Curtis, T. Dobrowolski, and J. Mogilski, Some applications of the topological characterizations of the sigmacompact spaces and , Trans. Amer. Math. Soc. 284 (1984), 837846. MR 743748 (86i:54035)
 [Du]
 J. Dugundji, Locally equiconnected spaces and absolute neighborhood retracts, Fund. Math. 57 (1965), 187193. MR 0184202 (32:1675)
 [Hu]
 S.T. Hu, Theory of retracts, Wayne State Univ. Press, Detroit, Mich., 1965. MR 0181977 (31:6202)
 [Ke]
 O. H. Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931), 748758. MR 1512740
 [Mo]
 J. Mogilski, Characterizing the topology of infinitedimensional compact manifolds, Proc. Amer. Math. Soc. 92 (1984), 111118. MR 749902 (85m:57012)
 [Sa]
 K. Sakai, Combinatorial infinitedimensional manifolds and manifolds, Topology Appl. (to appear).
 [Sa]
 , On topologies of triangulated infinitedimensional manifolds, J. Math. Soc. Japan 39 (1987) (in press). MR 879930 (88e:57020)
 [Sa]
 , Simplicial complexes triangulating infinitedimensional manifolds, preprint.
 [Sa]
 , Completions of metric simplicial complexes by using norms, preprint.
 [To]
 H. Toruńczyk, On CEimages of the Hilbert cube and characterization of manifolds, Fund. Math. 106 (1980), 3140. MR 585543 (83g:57006)
 [Wo]
 R. Y.T. Wong, Noncompact Hilbert cube manifolds, unpublished manuscript.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198708944536
PII:
S 00029939(1987)08944536
Keywords:
Simplicial complex,
combinatorial manifold,
metric topology,
localcompactification,
manifold,
manifold,
stable,
f.d. cap set,
set,
ANR
Article copyright:
© Copyright 1987 American Mathematical Society
