Curriculum Vitaes

MIYAZAKI KAZUMI

  (宮嵜 和美)

Profile Information

Affiliation
Professor, Institute of Education, Center of Advanced Education, Osaka Sangyo University
Degree
Doctor (Science)(Ehime University)
博士(理学)(愛媛大学)
Master (Education)(Osaka Kyoiku University)
修士(教育学)(大阪教育大学)

J-GLOBAL ID
200901057101001636
researchmap Member ID
6000010825

Papers

 13
  • Dikran Dikranjan, Kazumi Miyazaki, Tsugunori Nogura, Takamitsu Yamauchi
    TOPOLOGY AND ITS APPLICATIONS, 230 490-505, Oct, 2017  Peer-reviewed
    We study properties of the pseudocompact spaces X with a weak selection, and we dedicate a particular attention to the weak selection topologies on X. In case when X is also locally compact, we obtain a convenient decomposition of X into a finite union of clopen sets, which are either almost compact or connected with a remainder of size two in their Stone-Cech compactification. (C) 2017 Elsevier B.V. All rights reserved.
  • S. Garc, a-Ferreira, K. Miyazaki, T. Nogura, A. H. Tomita
    HOUSTON JOURNAL OF MATHEMATICS, vol 39(No.4) 1385-1399, Dec, 2013  Peer-reviewed
    A weak selection on an infinite set X is a function f : [X]2 → X such that f({x,y}) ∈ {x,y} for each {x,y} ∈ [X]2. A weak selection f on X defines a relation x f y if f({x,y}) = x whenever x,y ∈ X are distinct. The topology τf on X generated by the weak selection f is the one which has the family of all intervals (←x)f = {y ∈ X : y f x} and (x →)f = {y ∈ X : x f y} as a subbase. A weak selection on a space is said to be continuous if it is a continuous function with respect to the Vietoris topology on [X]2. The paper deals with topological spaces (X,τ) for which there is a set W of continuous weak selections satisfying τ = Vf∈W τf (we say that the topology of X is generated by continuous weak selections). We prove that for any infinite cardinal α, there exists a weakly orderable space whose topology cannot be generated by less than or equal to α-many continuous weak selections. We prove that any subspace of a space generated by continuous weak selections is also generated by continuous weak selections. Assuming that c is regular, we construct a suborderable space whose topology is generated by c-many continuous weak selections but not by less than c. Also, under the assumption of GCH, for every infinite successor cardinal α+ we construct a space X that is generated by α+-many continuous weak selections but cannot be generated by α-many selections. © 2013 University of Houston.
  • S. García-Ferreira, K. Miyazaki, T. Nogura
    Topology and its Applications, 160(18) 2465-2472, Dec 1, 2013  Peer-reviewed
    A weak selection on an infinite set X is a function σ:[X]2→X such that σ({x, y})∈{x, y} for each {x, y}∈[X]2. A weak selection on a space is said to be continuous if it is a continuous function with respect to the Vietoris topology on [X]2 and the topology on X. We study some topological consequences from the existence of a continuous weak selection on the product X×Y for the following particular cases:(i)Both X and Y are spaces with one non-isolated point.(ii)X is a space with one non-isolated point and Y is an ordinal space. As applications of the results obtained for these cases, we have that if X is the continuous closed image of suborderable space, Y is not discrete and has countable tightness, and X×Y admits a continuous weak selection, then X is hereditary paracompact. Also, if X is a space, Y is not-discrete and Sel2c(X×Y)≠θ, then X is totally disconnected. © 2013 Elsevier B.V.
  • Elise Grabner(Slippery Rock University, Gary Grabner(Slippery Rock University, Kazumi Miyazaki, Jamal Tartir(Youngstown, State University
    the International Journal of Pure and Applied Mathematics, 49(2) 251-278, 2008  Peer-reviewed
    relative propertyにおけるsemi-metricとrelative first countable 研究と結果
  • Elise Grabner(Slippery Rock University, Gary Grabner(Slippery Rock University, Kazumi Miyazaki, Jamal Tartir(Youngstown University
    Questions and Answers in General Topology, 25(1) 53-55, Apr, 2007  Peer-reviewed
    異なる3種類のrelative normal について、部分空間Yがどんな全空間の中においてもそれぞれのrelative normalになるときの特徴づけを示し、さらにrelative s-normalの場合には部分空間Yがcompactであるという同値条件を得た。これによりnormalの観点からのcompact 空間の利用範囲をさらに広げることができた。
  • E Grabner, G Grabner, K Miyazaki, J Tartir
    TOPOLOGY AND ITS APPLICATIONS, 153(5-6) 874-885, Dec, 2005  Peer-reviewed
    In their study of relative metric spaces, Arkhangel'skii and Gordienko introduce several relative properties of paracompactness type. We investigate the relationships between these properties and other relative properties of paracompactness type and answer two questions raised by Arkhangel'skii and Gordienko. Theorem. If Y is strongly regular in X and 3 paracompact in X then Y is star normal in X. Theorem. Y is strongly star normal in X if and only if Y is Aull paracompact in X. Corollary. If Y is strongly star normal in X then Y is 2-paracompact in X. Corollary. If Y is properly metrizable in X then Y is strongly star normal in X. (c) 2005 Published by Elsevier B.V.
  • Elise Grabner(Slippery Rock University, Gary Grabner(Slippery Rock University, Kazumi Miyazaki, Jamal Tartir(Youngstown University
    Questions and Answers in General Topology, 22(2) 91-104, Oct, 2004  Peer-reviewed
    これまで研究してきたrelative paracompact, relative metacompact, relative normal, rerative σ-paracompactの関係を集約、詳しく図式化しそれらの間にあるgapとしての多くの反例を示した。さらにこの時点で解明できていない問題を公表した。
  • Elise Grabner(Slippery Rock University, Gary Grabner(Slippery Rock University, Kazumi Miyazaki, Jamal Tartir(Youngstown University
    Applied General Topology, 5(2) 199-212, Sep, 2004  Peer-reviewed
    paracompact→collectionwise normal、metacompact + collectionwise normal→paracompactという2つのoriginal versionにおける関係を様々なrelative versionにおいて研究し、あるrelative collectionwise normalにおいては、はじめの図式が成り立たないという反例を示した。これによりoriginalでの常識が成り立つ境界を明らかにした。
  • Elise Grabner(Slippery Rock University, Gary Grabner(Slippery Rock University, Kazumi Miyazaki
    Topology Proceedings,, 25(2000 Summer) 145-177, May, 2002  Peer-reviewed
    relative paracompact,relative metacompactとoriginal versionのparacompact, matacompactを対比しこれを用いて他の性質への特徴づけを示した。さらに closurepreservingという観点から新しいrelative paracompactとrelative metacompact を定義し他のrelative propertyの中での位置と役割を示した。
  • S Fujii, K Miyazaki, T Nogura
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 54(2) 273-281, Apr, 2002  Peer-reviewed
    We prove that a countable regular space has a continuous selection if and only if it is scattered. Further we prove that a paracompact scattered space admits a continuous selection if each of its points has a countable pseudo-base. We also provide two examples to show that: (1) paracompactness can not be replaced by countable compactness even together with (collectionwise) normality, and (2) having countable pseudo-base at each of its points can not be omitted even in the class of regular Lindelof linearly ordered spaces.
  • Kazumi Miyazaki
    Scientiate Mathematicae Japonicae, 53(3) 489-494, May, 2001  Peer-reviewed
    「compact空間においてhyperspaceへのcontinuous selectionをもつ同値条件はorderableである」というvan MillとWattelのよく知られている結果の“compact”を“almost compact”に弱めても同じ結果が得られることを示し、他の位相を導入したhyperspaceにも同様の結果が得られることを示した。
  • K Miyazaki
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 129(9) 2777-2782, 2001  Peer-reviewed
    We give a characterization of countably paracompact and collectionwise normal spaces by means of set-valued semi-continuous selections. This provides a positive answer to a problem of V. Gutev.
  • Kazumi Miyazaki
    Mathematica Japonica, 50(1) 17-23, Jul, 1999  Peer-reviewed
    Michaelのparacompact spaceにおける可算な局所有限開細分を用いた特徴づけがrelative paracompactにおいてどこまで成り立つかを調べ、成り立たない場合の反例も示した。更にcompact, Lindelof, paracompact spaceをrelative paracompactを用いて特徴づけした。

Misc.

 1

Books and Other Publications

 2

Presentations

 10

Professional Memberships

 1

研究テーマ

 4
  • 研究テーマ(英語)
    Relative Property
    概要(英語)
    位相空間の性質に対する部分空間の性質の研究
    研究期間(開始)(英語)
    1995/04/01
  • 研究テーマ(英語)
    set-valued semi-continuous selection
    キーワード(英語)
    semi-continuous selection
    概要(英語)
    set-valued semi continuous selectionの存在による位相的性質の特徴付け
    研究期間(開始)(英語)
    1998/04/01
    研究期間(終了)(英語)
    2001/03/31
  • 研究テーマ(英語)
    continuous selection
    キーワード(英語)
    selection, hyperspace
    概要(英語)
    種々の空間のcontinuous selectionの存在の研究とそれを用いた位相的性質の特徴づけ
    研究期間(開始)(英語)
    1998/04/01
  • 研究テーマ(英語)
    weak selection,hyperspace
    研究期間(開始)(英語)
    2002/04/01