Publications of Katsuro S
AKAIBooks
• Geometric aspects of general topology. Springer Monographs in Mathematics. Tokyo, 2013: Springer (ISBN 978-4-431-54396-1/hbk; 978-4-431-54397-8/ebook). xv, 521 p.
Papers
1. On embeddings of infinite-dimensional manifold pairs, Sci. Rep. Tokyo Kyˆoiku Daigaku, Sect. A 12 (1974), 202–213.
2. An embedding of ℓ2-manifold pairs in ℓ2, J. Math. Soc. Japan 27 (1975), 557–560.
3. Embeddings of infinite-dimensional manifold pairs and remarks on stability and deficiency, J. Math. Soc. Japan 29 (1977), 261–280.
4. Replacing maps by embeddings between [0, 1)-stable Q-manifold pairs, Math. Japonica 22 (1977), 93–98.
5. An embedding theorem of infinite-dimensional manifold pairs in the model space, Fund. Math. 100(1978), 83–87.
6. Some properties of MAR and MANR, Tˆohoku Math. J. 30 (1978), 351–366.
7. Images of ℓ2-manifolds under approximate fibrations, Proc. Japan Acad., Ser. A 57 (1981), 260–261.
8. Stability for infinite-dimensional fibre bundles, Tsukuba J. Math. 5 (1981), 85–99.
9. The space of retractions of a compact Q-manifold is an ℓ2-manifold, Proc. Amer. Math. Soc. 83(1981), 421–424.
10. Homeomorphisms of infinite-dimensional fibre bundles, Tsukuba J. Math. 6 (1982), 21–33. 11. Boundaries and compliments of infinite-dimensional manifolds in the model space, Topology
Appl. 15 (1983), 79–91.
12. A characterization of local equiconnectedness, Pacific J. Math. 111 (1984), 231–241.
13. Each R∞-manifold has a unique piecewise linear R∞-structure, Proc. Amer. Math. Soc. 90 (1984), 616–618.
14. On R∞-manifolds and Q∞-manifolds, Topology Appl. 18 (1984), 69–79.
15. On R∞-manifolds and Q∞-manifolds II : Infinite-deficiency, Tsukuba J. Math. 8 (1984), 101–118.
16. Fine homotopy equivalences of simplicial complexes, Bull. Polish Acad. Sci., Math. 34 (1986), 89–97.
17. Combinatorial infinite-dimensional manifolds and R∞-manifolds, Topology Appl. 26 (1987), 43–64.
18. On topologies of triangulated infinite-dimensional manifolds, J. Math. Soc. Japan 39 (1987), 287–300.
19. Completions of metric simplicial complexes by using ℓp-norms, Topology Proc. 1986 11 (1987), 177–208.
20. The ℓ1-completion of a metric combinatorial ∞-manifold, Proc. Amer. Math. Soc. 100 (1987), 574–578.
21. A Q-manifold local-compactification of a metric combinatorial ∞-manifold, Proc. Amer. Math. Soc. 100 (1987), 775–780.
22. Simplicial complexes triangulating infinite-dimensional manifolds, Topology Appl. 29 (1988), 167–183.
23. The space of cross sections of a bundle, Proc. Amer. Math. Soc. 103 (1988), 956–960. 24. A mapping theorem infinite-dimensional manifolds and its generalizations, Colloq. Math. 56
(1988), 319–332.
25. (joint with Wong, R.Y.) Conjugating homeomorphisms to uniform homeomorphisms, Trans. Amer. Math. Soc. 311 (1989), 337–356.
26. (joint with Wong, R.Y.) The space of Lipschitz maps from a compactum to a locally convex set, Topology Appl. 32 (1989), 223–235.
27. (joint with Wong, R.Y.) On the space of Lipschitz homeomorphisms of a compact polyhedron, Pacific J. Math. 139 (1989), 195–207.
28. (joint with Wong, R.Y.) Infinite-dimensional manifold triples, Trans. Amer. Math. Soc. 318 (1990), 545–555.
29. A function space triple of a compact polyhedron into an open set in Euclidean space, Proc. Amer. Math. Soc. 108 (1990), 547–555.
30. (joint with Nguyen To Nhu and Wong, R.Y.) Spaces of retractions which are homeomorphic to Hilbert space, Fund. Math. 136 (1990), 45–52.
31. On hyperspaces of polyhedra, Proc. Amer. Math. Soc. 110 (1990), 1089–1097.
32. (joint with Wong, R.Y.) Manifold subgroups of the homeomorphism group of a compact Q- manifold, Pacific J. Math. 147 (1991), 165–185.
33. An embedding space triple of the unit interval into a graph and its bundle structure, Proc. Amer. Math. Soc. 111 (1991), 1171–1175.
34. The space of Lipschitz maps from a compactum to an absolute neighborhood LIP extensor, Fund. Math. 138 (1991), 27–34.
35. (joint with Eda, K.) A factor of singular homology, Tsukuba J. Math. 15 (1991), 351–387. 36. Connecting direct limit topologies with metrics on infinite-dimensional manifolds, Compositio
Math. 81 (1992), 237–245; A corrigendum, ibid. 102 (1996), 357.
37. (joint with Guo, B.-L.) The join of ANR’s for stratifiable spaces, Math. Japonica 38 (1993), 361–370.
38. (joint with Guo, B.-L.) Hyperspaces of CW-complexes, Fund. Math. 143 (1993), 23–40. 39. A Q∞-manifold topology of the space of Lipschitz maps, Topology Appl. 53 (1993), 7–18. 40. (joint with Nguyen To Nhu) The compact neighborhood extension property and local equi-
connectedness, Proc. Amer. Math. Soc. 121 (1994), 259–265.
41. Free actions of zero-dimensional compact groups on Menger manifolds, Proc. Amer. Math. Soc. 122 (1994), 647–648.
42. All autohomeomorphisms of connected Menger manifolds are stable, Proc. Amer. Math. Soc. 122(1994), 1289–1291.
43. (joint with Iwamoto, Y.) A mapping theorem for Q-manifolds and µn+1-manifolds, Bull. Polish Acad. Sci., Math. 42 (1994), 243–250.
44. (joint with Cauty, R. and Guo, B.-L.) The hyperspace of finite subsets of a stratifiable space, Fund. Math. 147 (1995), 1–9.
45. (joint with Wong, R.Y.) Manifolds of Lipschitz maps, Houston J. Math. 21 (1995), 557–568. 46. (joint with Guo, B.-L.) Spaces of measures on stratifiable spaces, Kobe J. Math. 12 (1995),
161–173.
47. (joint with Nguyen To Nhu) Probability measure functors preserving infinite-dimensional spaces, Colloq. Math. 70 (1996), 291–304.
48. (joint with Dobrowolski, T.) Spaces of measures on metrizable spaces, Topology Appl. 72 (1996), 215–258.
49. (joint with Akaike, Y.) The complement theorem in n-shape theory for compact pairs, Glasnik Mat., Ser. III 31 (1996), 307–319.
50. Semi-free actions of zero-dimensional compact groups on Menger compacta, Proc. Amer. Math. Soc. 125 (1997), 2809–2813.
51. (joint with Uehara, S.) A Q-manifold compactification of the homeomorphism group of a graph, Bull. Polish Acad. Sci., Math. 45 (1997), 281–286.
52. Proper n-shape categories, Glasnik Mat., Ser. III 33 (1998), 287–297.
53. (joint with Akaike, Y.) Describing the proper n-shape category by using non-continuous func- tions, Glasnik Mat., Ser. III 33 (1998), 299–321.
54. (joint with Uehara, S.) A Hilbert cube compactification of the Banach space of continuous functions, Topology Appl. 92 (1999), 107–118.
55. (joint with Uehara, S.) Spaces of upper semi-continuous multi-valued functions on complete metric spaces, Fund. Math. 160 (1999), 199–218.
56. (joint with Banakh, T.) Characterizations of (R∞, σ)- or (Q∞,Σ)-manifolds and thier ap- plications, Topology Appl. 106 (2000), 115–134.
57. (joint with Banakh, T.) Free topological semilattices homeomorphic of R∞and Q∞, Topology Appl. 106 (2000), 135–147.
58. (joint with Uehara, S.) Spaces of upper semi-continuous multi-valued functions on separable metric spaces, Tsukuba J. Math. 24 (2000), 69–80.
59. The completion of metric ANR’s and homotopy dense subsets, J. Math. Soc. Japan 52 (2000), 835–846.
60. (joint with Banakh, T. and Kawamura, K.) The direct limits of the Banach-Mazur compacta, Bull. London Math. Soc. 32 (2000), 709–717.
61. (joint with Iwamoto, Y.) Strong n-shape theory, Topology Appl. 122 (2002), 253–267.
62. An alternative proof of Cauty-Geoghegan’s chatacterization of ANR’s, Topology Appl. 122 (2002), 407–414.
63. (joint with Yang, Z.) Hyperspaces of non-compact metrizable spaces which are homeomorphic to the Hilbert cube, Topology Appl. 127 (2002), 331–342.
64. (joint with Banakh, T. and Kurihara, M.) Hyperspaces of normed linear spaces with the Attouch-Wets topology, Set-Valued Analysis 11 (2003), 21–36.
65. (joint with Yang, Z.) The space of limits of continua in the Fell topology, Houston J. Math. 29(2003), 325–335.
66. (joint with Yaguchi, M.) Characterizing manifolds modeled on certain dense subspaces of non-separable Hilbert spaces, Tsukuba J. Math. 27 (2003), 143–159.
67. (joint with Yaguchi, M.) Hyperspaces of Banach spaces with Attouch-Wets topology, Set- Valued Analysis 12 (2004), 329–344.
68. (joint with Kubi´s, W. and Yaguchi, M.) Hyperspaces of separable Banach spaces with the Wijsman topology, Topology Appl. 148 (2005), 7–32.
69. (joint with Kurihara, M. and Yaguchi, M.) Hyperspaces with the Hausdorff metric and uni- form ANR’s, J. Math. Soc. Japan 57 (2005), 523–535.
70. (joint with Mine, K. and Yaguchi, M.) Hyperspaces of finite sets in universal spaces for absolute Borel classes, Bull. Polish Acad. Sci., Math. 53 (2005), 409–419.
71. (joint with Uehara, S.) Topological structure of the space of lower semi-continuous functions, Comment. Math. Univ. Carolinae 47 (2006), 113–126.
72. (joint with Yaguchi, M.) The AR-property of the space of closed convex sets, Colloq. Math., 106(2006), 15–24.
73. (joint with Yang, Z.) Hyperspaces of closed convex sets in Euclidean spaces with the Fell topology, Bull. Polish Acad. Sci., Math. 55 (2007), 139–143.
74. (joint with Kubi´s, W.) Hausdorff hyperspaces of Rn and their dense subspaces, J. Math. Soc. Japan 60 (2008), 193–217.
75. The spaces of compact convex sets and bounded closed convex sets in a Banach space, Houston J. Math. 34 (2008), 289–300.
76. (joint with Mine, K.) Open subsets of LF-spaces, Bull. Polish Acad. Sci., Math. 56 (2008), 25–37.
77. (joint with Banakh, T. and Mine, K.) Topological classification of homeomorphism groups of infinite graphs, Topology Appl. 156 (2009), 2845–2869.
78. (joint with Kogasaka, A.) A Hilbert cube compactification of the function space with the compact-open topology, Central Euro. J. Math. 7 (2009), 670–682.
79. (joint with Banakh, T., Mine, K. and Yagasaki, T.) Spaces of continuous maps from non- compact spaces into topological groups with the Whitney topology, Topology Appl. 157 (2010), 1110–1117.
80. (joint with Banakh, T., Mine, K. and Yagasaki, T.) Homeomorphism and diffeomorphism groups of non-compact manifolds with the Whitney topology, Topology Proc. 37 (2011), 61– 93.
81. (joint with Mine, K.) Simplicial complexes and open subsets of non-separable LF-spaces, Canad. J. Math. 63 (2011), 436–459.
82. (joint with Mine, K., Yagasaki, T. and Yamashita, A.) Topological type of the group of uniform homeomorphisms of the real line, Topology Appl. 158 (2011), 572–581.
83. Small subdivision of simplicial complexes with the metric topology, J. Math. Soc. Japan 63 (2011), 789–800.
84. Correcting Taylor’s cell-like map, Glasnik Mat., Ser. III 46 (2011), 483–487.
85. (joint with Mine, K.) Subdivision of simplicial complexes preserving the metric topology, Canad. Math. Bull. 54 (2012), 157–163.
86. (joint with Yang, H.) The box topology of infinite simplicial complexes, Tsukuba J. Math. 36 (2012), 295–309.
87. (joint with Banakh, T., Mine, K., Repovˇs, D. and Yagasaki, T.) Detecting topological groups which are (locally) homeomorphic to LF-spaces, Topology Appl. 160 (2013), 2272–2284. 88. (joint with Banakh, T. and Hetman, I.) Recognizing the topology of the space of closed convex
subsets of a Banach space, Stud. Math. 216 (2013), 17–33.
89. (joint with Banakh, T., Mine, K. and Yagasaki, T.) On homeomorphism groups of non- compact surfaces, endowed with the Whitney topology, Topology Appl. 164 (2014), 170-181. 90. (joint with Koshino, K.) A Hilbert cube compactification of a function space from a Peano space into a one-dimensional locally compact absolute retract, Topology Appl. 161 (2014), 37-57.
91. (joint with Koshino, K. and Yang, H.) A function space from a compact metrizable space to a dendrite with the hypo-graph topology, Central Euro. J. Math. (to appear).
