高等教育センター

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。

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