On topologies of triangulated infinite-dimensional manifolds

Katsuro SAKAI

doi:10.2969/jmsj/03920287

Katsuro SAKAI

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 2 Pages 287-300

DOI https://doi.org/10.2969/jmsj/03920287

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Published: 1987 Received: September 07, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Bestvina, P. L. Bower, J. Mogilski and J. J. Walsh, Characterization of Hilbert space manifolds revisited, Topology Appl., 24 (1986), 53-69.
2) T. A. Chapman, Four classes of separable metric infinite-dimensional manifolds, Bull. Amer. Math. Soc., 76 (1970), 399-403.
3) D. W. Curtis, Boundary sets in the Hilbert cube, Topology Appl., 20 (1985), 201-221.
4) D. W. Curtis, Hyperspaces of finite subsets as boundary sets, Topology Appl., 22 (1986), 97-107.
5) D. W. Curtis, T. Dobrowolski and J. Mogilski, Some applications of the topological characterizations of the sigma-compact spaces l²_f and ∑, Trans. Amer. Math. Soc., 284 (1984), 837-846.
6) C. H. Dowker, Topology of metric complexes, Amer. J. Math., 74 (1952), 555-577.
7) W. E. Haver, Mappings between ANR's that are fine homotopy equivalences, Pacific J. Math., 58 (1975), 457-461.
8) R. E. Heisey, Manifolds modelled on R^∞ or bounded weak-* topologies, Trans. Amer. Math. Soc., 206 (1975), 295-312.
9) R. E. Heisey and H. Torunczyk, On the topology of direct limits of ANR's, Pacific J. Math., 93 (1981), 307-312.
10) D. W. Henderson, Z-sets in ANR's, Trans. Amer. Math. Soc., 213 (1975), 205-216.
11) D. W. Henderson and J. E. West, Triangulated infinite-dimensional manifolds, Bull. Amer. Math. Soc., 76 (1970), 655-660.
12) J. P. Henderson and J. J. Walsh, Examples of cell-like decompositions of the infinite-dimensional manifolds σ and ∑, Topology Appl., 16 (1983), 143-154.
13) S.-T. Hu, Theory of Retracts, Wayne State Univ. Press, Detroit, 1965.
14) J. Mogilski, Characterizing the topology of infinite-dimensional σ-compact manifolds, Proc. Amer. Math. Soc., 92 (1984), 111-118.
15) K. Sakai, Embeddings of infinite-dimensional manifold pairs and remarks on stability and deficiency, J. Math. Soc. Japan, 29 (1977), 262-280.
16) K. Sakai, On R^∞-manifolds and Q^∞-manifolds, Topology Appl., 18 (1984), 69-80.
17) K. Sakai, On R^∞-manifolds and Q^∞-manifolds, II: Infinite deficiency, Tsukuba J. Math., 8 (1984), 101-118.
18) K. Sakai, Combinatorial infinite-dimensional manifolds and R^∞-manifolds, to appear in Topology Appl.
19) K. Sakai, Fine homotopy equivalences of simplicial complexes, Bull. Acad. Polon. Sci., 34 (1986), 89-97.
20) H. Torunczyk, A correction of two papers concerning Hilbert manifolds, Fund. Math., 125 (1985), 89-93.
21) M. M. Zaricinyi, Infinite-dimensional manifolds which arise from the direct limits of ANR's (in Russian), Uspekhi Mat. Nauk, 39 (1984), 153-154; English transl. in Russian Math. Surveys.
22) K. Sakai, Simplicial complexes triangulating infinite-dimensional manifolds, preprint.

Right : [1] M. Bestvina, P. L. Bower, J. Mogilski and J. J. Walsh, Characterization of Hilbert space manifolds revisited, Topology Appl., 24 (1986), 53-69.
[2] T. A. Chapman, Four classes of separable metric infinite-dimensional manifolds, Bull. Amer. Math. Soc., 76 (1970), 399-403.
[3] D. W. Curtis, Boundary sets in the Hilbert cube, Topology Appl., 20 (1985), 201-221.
[4] D. W. Curtis, Hyperspaces of finite subsets as boundary sets, Topology Appl., 22 (1986), 97-107.
[5] D. W. Curtis, T. Dobrowolski and J. Mogilski, Some applications of the topological characterizations of the sigma-compact spaces l²_f and ∑, Trans. Amer. Math. Soc., 284 (1984), 837-846.
[6] C. H. Dowker, Topology of metric complexes, Amer. J. Math., 74 (1952), 555-577.
[7] W. E. Haver, Mappings between ANR's that are fine homotopy equivalences, Pacific J. Math., 58 (1975), 457-461.
[8] R. E. Heisey, Manifolds modelled on R^∞ or bounded weak-^* topologies, Trans. Amer. Math. Soc., 206 (1975), 295-312.
[9] R. E. Heisey and H. Torunczyk, On the topology of direct limits of ANR's, Pacific J. Math., 93 (1981), 307-312.
[10] D. W. Henderson, Z-sets in ANR's, Trans. Amer. Math. Soc., 213 (1975), 205-216.
[11] D. W. Henderson and J. E. West, Triangulated infinite-dimensional manifolds, Bull. Amer. Math. Soc., 76 (1970), 655-660.
[12] J. P. Henderson and J. J. Walsh, Examples of cell-like decompositions of the infinite-dimensional manifolds σ and ∑, Topology Appl., 16 (1983), 143-154.
[13] S. -T. Hu, Theory of Retracts, Wayne State Univ. Press, Detroit, 1965.
[14] J. Mogilski, Characterizing the topology of infinite-dimensional σ-compact manifolds, Proc. Amer. Math. Soc., 92 (1984), 111-118.
[15] K. Sakai, Embeddings of infinite-dimensional manifold pairs and remarks on stability and deficiency, J. Math. Soc. Japan, 29 (1977), 262-280.
[16] K. Sakai, On R^∞-manifolds and Q^∞-manifolds, Topology Appl., 18 (1984), 69-80.
[17] K. Sakai, On R^∞-manifolds and Q^∞-manifolds, II: Infinite deficiency, Tsukuba J. Math., 8 (1984), 101-118.
[18] K. Sakai, Combinatorial infinite-dimensional manifolds and R^∞-manifolds, to appear in Topology Appl.
[19] K. Sakai, Fine homotopy equivalences of simplicial complexes, Bull. Acad. Polon. Sci., 34 (1986), 89-97.
[20] H. Torunczyk, A correction of two papers concerning Hilbert manifolds, Fund. Math., 125 (1985), 89-93.
[21] M. M. Zaricinyi, Infinite-dimensional manifolds which arise from the direct limits of ANR's (in Russian), Uspekhi Mat. Nauk, 39 (1984), 153-154; English transl. in Russian Math. Surveys.
[22] K. Sakai, Simplicial complexes triangulating infinite-dimensional manifolds, preprint.

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