Nobuyuki KEMOTO


Department of Mathematics
Oita University

How to contact me

Education

Research Interests

  Now I'm interested in topological properties of product spaces, in particular products of ordinals. It is well known that $\omega_1^2$ is countably paracomapct and normal and that $\omega_1\times (\omega_1+1)$ is countably paracompact but not normal. We (with Ohta and Tamano 1993) proved that for every subspaces $A$ and $B$ of $\omega_1$, normality of $A\times B$ is equivalent to countable paracompactness and that $A\times B$ is not normal if $A$ and $B$ are disjoint stationary sets in $\omega_1$.
  It is also well known that a space $X$ is normal and countably paracompact iff $X\times (\omega+1)$ is normal. Note that countable paracompactness implies countable metacompactness and that for normal spaces, countable paracompactness and countable metacompactness are equivalent. A normal not countably paracompact space is called a Dowker space. We (with Smith 1996) proved that products of two ordinals are hereditarily countably metacompact. So there does not exist a Dowker subspace of $\omega_1^2$.
  One of my interests is:

Problem 1. Are countably paracompact subspaces of $\omega_1^2$ normal?

  We (with Smith and Szeptycki 2000) had a partial answer that assuming V=L, Problem 1 is affirmative. I still beieve there is a counterexample of Problem 1 in some model of set theory.   We (with Smith 1997) proved that $\omega_1^n$ is hereditarily countably metacompact for every natural number $n$, but there is a subspace of the infinite product space $\omega_1^\omega$ which is not countably metacompact. Recently W. G. Fleissner (200?) proved that products of finitely many ordinals are hereditarily countably metacompact. So there is no Dowker subspace of products of finitely many ordinals. The classical Dowker space constructed by M. E. Rudin is a subspace of the box product space of $\omega_n$'s. My second interest is:

Problem 2. Does there exist a Dowker subspace of the (box) product space $\omega_1^\omega$?

Publications

  1. Yasushi Hirata, Nobuyuki Kemoto and Haruto Ohta, $C^*$-embedded dense subsets of $z$-neighborhood-sublinear spaces are $P$-embedded, Top. Proc., 62 (2023) 99-116.
  2. Nobuyuki Kemoto and Toshimichi Usuba, $C^*$-embedding and $P$-embedding in subspaces of products of ordinals, Top. Appl., 318 (2022), Paper No. 108194, 9pp.
  3. Nobuyuki Kemoto, Completeness of lexicographic products, Top. Proc., 58 (2021) 105-123.
  4. Y. Hirata and N. Kemoto, The weight of lexicographic products, Top. Appl., 284 (2020), Paper No. 107357, 13 pp.
  5. Y. Hirata and N. Kemoto, A characterization of paracompactness of lexicographic products, Top. Proc., 56 (2020) 85-95.
  6. Nobuyuki Kemoto, Countable compactness of lexicographic products of GO-spaces, Comment. Math. Univ. Carol., 60 (2019) 421-439.
  7. Nobuyuki Kemoto, Hereditary paracompactness of lexicographic products, Top. Proc., 53 (2019) 301-317.
  8. Nobuyuki Kemoto, Paracompactness of Lexicographic products of GO-spaces, Top. Appl., 240 (2018) 35-58.
  9. Nobuyuki Kemoto, The structure of the linearly ordered compactifications, Top. Proc., 52 (2018) 189-204.
  10. Nobuyuki Kemoto, Lexicographic products of GO-spaces, Top. Appl., 232 (2017) 267-280.
  11. Nobuyuki Kemoto, Normality, orthocompactness and countable paracompactness of products of GO-spaces, Top. Appl., 231 (2017) 276-291.
  12. Nobuyuki Kemoto, Orderability of products , Top. Proc., 50 (2017) 67-78.
  13. Yasushi Hirata and Nobuyuki Kemoto, Countable metacompactness of products of LOTS' , Top. Appl., 178 (2014) 1-16.
  14. Yasushi Hirata, Nobuyuki Kemoto and Yukinobu Yajima, Products of monotonically normal spaces with various special factors , Top. Appl., 164 (2014) 45-86.
  15. N. Kemoto, Y. F. Ortiz-Castillo and R. Rojas-Hernandez, On $C$-embeddedness of Hyperspaces, Top. Appl., 162 (2014) 34-42.
  16. N. Kemoto, The lexicographic ordered products and the usual Tychonoff products, Top. Appl., 162 (2014) 20-33.
  17. Y. Hirata and N. Kemoto, Orthocompactness versus normality in hyperspaces, Top. Appl., 159 (2012) 1169-1176.
  18. N. Kemoto, Erratum to: ``Normality and countable paracompactness of hyperspaces of ordinals", Topology and its Applications 154 (2007) 358-362., Top. Appl., 157 (2010) 2446-2447.
  19. N. Kemoto and J. Terasawa, Strong zero-dimensionality of hyperspaces, Top. Appl.,157 (2010) 2376-2382.
  20. Y. Hirata and N. Kemoto, Orderability of subspaces of well-orderable topological spaces, Top. Appl., 157 (2010) 127-135.
  21. N. Kemoto and Y. Yajima, Certain sequences with compact closure, Top. Appl., 156 (2009) 1348-1354.
  22. N. Kemoto and Y. Yajima, Rectangular Products with ordinal factors, Top. Appl., 154 (2007) 758-770.
  23. N. Kemoto, Normality and countable paracompactness of hyperspaces of ordinals, Top. Appl., 154 (2007) 358-362.
  24. N. Kemoto, $\sigma$-collectionwise Hausdorffness at singular strong limit cardinals, Top. Appl., 153 (2006) 1500-1506.
  25. Y. Hirata and N. Kemoto, Mild normality of finite products of subspaces of $\omega_1$, Top. Appl., 153 (2006) 1203-1213.
  26. Y. Hirata and N. Kemoto, The hereditarily collectionwise Hausdorff property in products of $\omega_1$, Top. Proc., 29 (2005) 167-173.
  27. N. Kemoto and P. J. Szeptycki, Countable paracompactness of $\sigma$-products, Top. Appl., 149 (2005) 259-271.
  28. N. Kemoto and P. J. Szeptycki, Topological properties of products of ordinals, Top. Appl., 143 (2004) 257-277.
  29. Y. Hirata and N. Kemoto, Separating by $G_{\delta}$-sets in finite powers of $\omega_1$, Fund. Math., 177 (2003) 83-94.
  30. W. G. Fleissner, N. Kemoto and J. Terasawa, Strong Zero-dimensionality of Products of Ordinals, Top. Appl., 132 (2003) 109--127.
  31. N. Kemoto, Higher separation axioms, Encyclopedia of General Topology, Ed. by K. P. Hart, J. Nagata and J. E. Vaughan, Elsevier Science, (2003) 149--152.
  32. L. Kalantan and N. Kemoto, Mild normality in products of ordinals, Houston J. Math, 29(4) (2003) 937-947.
  33. N. Kemoto, Subnormality in $\omega_1^2$, Top. Appl., 122 (2002) 287-296.
  34. N. Kemoto and T. Nogura, Normality and paranormality in product spaces, Top. Appl., 121 (2002) 319-331.
  35. N. Kemoto and K. Kuwaoka, ParaLindel\" of subspaces in products of two ordinals, Scientiae Mathematicae Japonicae, 54 (2001) 369--381.
  36. N. Kemoto, K. D. Smith and P. J. Szeptycki, Countable paracompactness versus normality in $\omega_1^2$, Top. Appl., 104 (2000) 141--154.
  37. N. Kemoto, K. Tamano and Y. Yajima, Generalized paracompactness of subspaces in products of two ordinals, Top. Appl., 104 (2000) 155--168.
  38. R. Fri\v c and N. Kemoto, Sequential completeness of products of ordinals, Czec. Math. 49 (1999) 119-125.
  39. N. Kemoto, Orthocompact subspaces in products of two ordinals, Top. Proc. 22 (1997), 247-264.
  40. N. Kemoto and Y. Yajima, Submetacompactness in $\beta$-spaces, Top. Proc. 22 (1997) 265-280.
  41. N. Kemoto, T. Nogura, K. D. Smith and Y. Yajima, Normal subspaces in products of two ordinals, Fund. Math. 151 (1996) 279-297.
  42. N. Kemoto and K. D. Smith, Hereditarily countable metacompactness in finite and infinite product spaces of ordinals, Top. Appl.77 (1997) 57-63.
  43. N. Kemoto and K. D. Smith, The product of two ordinals is hereditarily countably metacompact, Top. Appl. 74 (1996) 91-96.
  44. N. Kemoto, T. Nogura and Y. Yajima, Normality and closed projections of products with a cardinal factor, Top. Appl. 69 (1996) 217-226.
  45. N. Kemoto and Y. Yajima, Remarks on normality of $\Sigma$-products, Top. Proc. 19 (1994) 161--168.
  46. N. Kemoto and Y. Yajima, Orthocompactness in infinite product spaces, Proc. AMS 120 (1994) 591--596.
  47. N. Kemoto, Normality of products of GO-spaces and cardinals, Top. Proc. 18 (1993) 133-142.
  48. T. Miwa and N. Kemoto, Linearly ordered extensions of GO-spaces, Top. Appl. 54 (1993) 133-140.
  49. N. Kemoto and Y. Yajima, Orthocompactness and normality of products with a cardinal factor, Top. Appl. 49 (1993) 141-148.
  50. N. Kemoto and Y. Yajima, Orthocompactness in products, Tsukuba J. Math. 16 (1992) 407-422.
  51. N. Kemoto, H. Ohta and K. Tamano, Products of spaces of ordinal numbers, Top. Appl. 45 (1992) 245-260.
  52. N. Kemoto, Paracompactness in perfect, locally Lindel\"of spaces, Rocky Mount. J. Math. 22 (1992), 1-18.
  53. N. Kemoto, Collectionwise Hausdorffness at limit cardinals, Fund. Math. 138 (1991) 59-67.
  54. N. Kemoto, The shrinking property of products of cardinals, Fund. Math. 137 (1990) 59-63.
  55. N. Kemoto, Characterizations of expandability and the $\frak B$-property, Ind. J. Pure Appl. Math. 21 (1990), 923-933.
  56. N. Kemoto, Weak $[\omega_1,\infty)^r$-refinability in ordered spaces, Ind. J. Pure Appl. Math. 21 (1990) 116-119.
  57. N. Kemoto, Separations in spaces having the $\frak B$-property, Math. Japonica 35 (1990) 87-95.
  58. N. Kemoto, On $\frak B$-property, Q \& A in Gene. Top. 7 (1989) 71-79.
  59. N. Kemoto, Stationary subspaces in ordered spaces, Bull. Austral. Math. Soc 40 (1989) 381-387.
  60. N. Kemoto, The shrinking property and the $\frak B$-property in ordered spaces, Fund. Math. 134 (1989) 253-259.
  61. N. Kemoto, A note on connected submetaLindel\"of spaces, Bull. Austral. Math. Soc. 40 (1989) 83-89.
  62. N. Kemoto, Subparacompactness in locally nice spaces, Fund. Math. 132 (1989) 163-169.
  63. N. Kemoto, Topological or set theoretical assertions which are equivalent to $2^\kappa < 2^{\kappa^+}$, Bull. Coll. Ed. Univ. Ryukyus 33 (1988) 335-341.
  64. N. Kemoto, On questions of Hdeib, Q \& A in Gene. Top. 6 (1988) 157-162.
  65. N. Kemoto, A note on separable normal $\aleph$-spaces, Q \& A in Gene. Top. 6 (1988) 149-156.
  66. N. Kemoto, On Pareek's questions, Q \& A in Gene. Top. 6 (1988) 141-148.
  67. N. Kemoto, On Hattori's questions, Q \& A in Gene. Top. 6 (1988) 135-141.
  68. N. Kemoto, Consistency results on locally connected submetaLindel\"of normal spaces, Math. Japonica 33 (1988) 393-402.
  69. N. Kemoto, A note on rim-Lindel\"of locally connected normal Moore spaces, Top. Proc. 12 (1987) 199-208.
  70. N. Kemoto, A note on the normality of $\kappa$-trees with the tree topology, Bull. Coll. Ed. Univ. Ryukyus 31 (1987) 317-322.
  71. N. Kemoto, New subspaces of extensions, connectedness and local connectedness, Ind. J. Pure Appl. Math. 18 (1987) 234-247.
  72. N. Kemoto, Characterization of the existence of $\kappa$-Souslin trees, Bull. Coll. Ed. Univ. Ryukyus 27 (1984) 127-130.
  73. N. Kemoto, A proposition on the cardinality of closed discrete subsets of a topoological space, Proc. Japan Acad. 59 (1983) 130-131.
  74. N. Kemoto, Compacifications and Set Theoretic Topology（doctorial thesis）, Kobe University (1983).
  75. N. Kemoto, A characterization of the existence of a Souslin line, Bull. Austral. Math. Soc. 25 (1982) 425-431.
  76. N. Kemoto, On the local connectedness of $\beta X$, Bull. Soc. Royale Sci. Liege 50 (1981) 185-194.
  77. N. Kemoto, There is no remote point in $\mu X-X$, Math. Semi. Notes (Kobe J.) 8 (1980) 569-572.
  78. N. Kemoto, Another characterization of the point of $\beta X$, Math. Semi. Notes (Kobe J.) 8 (1980) 547-552.

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Author: Nobuyuki KEMOTO