The -completion of a metric combinatorial -manifold

Author:
Katsuro Sakai

Journal:
Proc. Amer. Math. Soc. **100** (1987), 574-578

MSC:
Primary 57N20; Secondary 54E52, 57Q05

DOI:
https://doi.org/10.1090/S0002-9939-1987-0891166-1

MathSciNet review:
891166

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a simplicial complex. The realization of admits the metric

**[An]**R. D. Anderson,*On sigma-compact subsets of infinite-dimensional spaces*, unpublished manuscript.**[Ch]**T. A Chapman,*Dense sigma-compact subsets of infinite-dimensional manifolds*, Trans.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]**-,*Lectures on Hilbert cube manifolds*, CBMS Regional Conf. Ser. in Math., no. 28, Amer. Math. Soc., Providence, R.I., 1976. MR**0423357 (54:11336)****[He]**D. W. Henderson,*Infinite-dimensional manifolds are open subsets of Hilbert space*, Bull. Amer. Math. Soc.**75**(1969), 759-762. MR**0247634 (40:898)****[Hu]**S.-T. Hu,*Theory of retracts*, Wayne State Univ. Press., Detroit, Mich., 1965. MR**0181977 (31:6202)****[Sa]**K. Sakai,*Combinatorial infinite-dimensional manifolds and**-manifolds*, Topology Appl.**26**(1987), in press. MR**893803 (88f:57027)****[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*, Topology Proc.**11**(1986).**[Sa]**-,*A**-manifold local-compactification of a metric combinatorial**-manifold*, Proc. Amer. Math. Soc.**100**(1987), in press.**[To]**H. Toruńczyk,*On CE-images of the Hilbert cube and characterization of**-manifolds*, Fund. Math.**106**(1980), 31-40. MR**585543 (83g:57006)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0891166-1

Keywords:
Simplicial complex,
combinatorial -manifolds,
the metric topology,
completion,
-manifold,
-manifold,
-manifold,
(f.d.) cap set,
-set

Article copyright:
© Copyright 1987
American Mathematical Society