A -manifold local-compactification of a metric combinatorial -manifold

Author:
Katsuro Sakai

Journal:
Proc. Amer. Math. Soc. **100** (1987), 775-780

MSC:
Primary 57N20; Secondary 54E45, 54F40, 57Q15

DOI:
https://doi.org/10.1090/S0002-9939-1987-0894453-6

MathSciNet review:
894453

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a combinatorial -manifold, that is, a countable simplicial complex such that the star of each vertex is combinatorially equivalent to the countable-infinite 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 local-compactification of which is a -stable -manifold containing as an f.d. cap set.

**[An]**R. D. Anderson,*On sigma-compact subsets of infinite-dimensional spaces*, unpublished manuscript.**[Ch]**T. A. Chapman,*Dense sigma-compact subsets of infinite-dimensional manifolds*, Trans. Amer. Math. Soc.**154**(1971), 399-426. MR**0283828 (44:1058)****[Ch]**--,*On the structure of Hilbert cube manifolds*, Compositio Math.**24**(1972), 329-353. MR**0305432 (46:4562)****[CDM]**D. W. Curtis, T. Dobrowolski, and J. Mogilski,*Some applications of the topological characterizations of the sigma-compact spaces**and*, Trans. Amer. Math. Soc.**284**(1984), 837-846. MR**743748 (86i:54035)****[Du]**J. Dugundji,*Locally equiconnected spaces and absolute neighborhood retracts*, Fund. Math.**57**(1965), 187-193. 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), 748-758. MR**1512740****[Mo]**J. Mogilski,*Characterizing the topology of infinite-dimensional**-compact manifolds*, Proc. Amer. Math. Soc.**92**(1984), 111-118. MR**749902 (85m:57012)****[Sa]**K. Sakai,*Combinatorial infinite-dimensional manifolds and**-manifolds*, Topology Appl. (to appear).**[Sa]**-,*On topologies of triangulated infinite-dimensional manifolds*, J. Math. Soc. Japan**39**(1987) (in press). MR**879930 (88e:57020)****[Sa]**-,*Simplicial complexes triangulating infinite-dimensional manifolds*, preprint.**[Sa]**-,*Completions of metric simplicial complexes by using**-norms*, preprint.**[To]**H. Toruńczyk,*On CE-images of the Hilbert cube and characterization of**-manifolds*, Fund. Math.**106**(1980), 31-40. MR**585543 (83g:57006)****[Wo]**R. Y.-T. Wong,*Non-compact Hilbert cube manifolds*, unpublished manuscript.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
57N20,
54E45,
54F40,
57Q15

Retrieve articles in all journals with MSC: 57N20, 54E45, 54F40, 57Q15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0894453-6

Keywords:
Simplicial complex,
combinatorial -manifold,
metric topology,
localcompactification,
-manifold,
-manifold,
-stable,
f.d. cap set,
-set,
ANR

Article copyright:
© Copyright 1987
American Mathematical Society