トップ研究者を探すコンパクト型可換群の構造及びMarkov稠密性を実現する群位相の導入の研究

コンパクト型可換群の構造及びMarkov稠密性を実現する群位相の導入の研究

KAKEN 科学研究費助成事業データベース で見る
研究課題番号 KAKENHI-PROJECT-26400091
研究種目 基盤研究(C)
研究分野 理工系
数物系科学
数学
幾何学
研究機関 愛媛大学
代表研究者 D・B Shakhmatov
研究期間 開始年月日 2014/4/1
研究期間 終了年度 2017
研究ステータス 完了 (2017/4/1)
配分額(合計) 4,810,000 (直接経費 :3,700,000、間接経費 :1,110,000)
配分額(履歴) 2017年度:1,430,000 (直接経費 :1,100,000、間接経費 :330,000)
2016年度:1,430,000 (直接経費 :1,100,000、間接経費 :330,000)
2015年度:1,300,000 (直接経費 :1,000,000、間接経費 :300,000)
2014年度:650,000 (直接経費 :500,000、間接経費 :150,000)
キーワード 位相群
トポロジー
代数学
コンパクト
連結性
小部分群
疑コンパクト
topological group
pseudocompact
selective property
variety of groups
reflexive group
SSGP group
divisible rank
MinAP group
sequentially compact
omega-bounded group
weakly pseudocompact
completeness properties
direct products
direct sums
topological vector space
dual group
multiplier convergence
compact
connected space
Markov problem
unconditionally closed
abelian group
group topology
precompact group
minimal group

研究成果

[雑誌論文] The impact of the Bohr topology on selective pseudocompactness

D. Shakhmatov, V.H. Yanez 2018

[雑誌論文] Two open-point games related to selective (sequential) pseudocompactness, with application to 1-cl-starcompactness property of Matveev

A. Dorantes-Aldama, D. Shakhmatov 2018

[学会発表] A factorization theorem for weak alpha-favourability

D. Shakhmatov 2018

[雑誌論文] Topological groups with many small subgroups revisited

D. Shakhmatov, V.H. Yanez 2018

[雑誌論文] SSGP topologies on abelian groups of positive finite divisible rank

D. Shakhmatov, V.H. Yanez 2018

[雑誌論文] Selectively sequentially pseudocompact group topologies on torsion and torsion-free Abelian groups

A. Dorantes-Aldama, D. Shakhmatov 2017

[雑誌論文] Completeness and compactness properties in metric spaces, topological groups and function spaces

Alejandro Dorantes-Aldama and Dmitri Shakhmatov 2017

[学会発表] Topological groups which are hard to come by

D. Shakhmatov 2017

[学会発表] Compactness properties defined by an open-point game

D. Shakhmatov 2017

[雑誌論文] The existence of continuous weak selections and orderability-type properties in products and filter spaces

K. Motooka, D. Shakhmatov, T. Yamauchi 2017

[学会発表] Minimal almost periodic topologies on groups

D. Shakhmatov 2017

[学会発表] Compactness-like properties defined by open-point games and maximal almost disjoint families

D. Shakhmatov 2017

[雑誌論文] Selective sequential pseudocompactness

Alejandro Dorantes-Aldama and Dmitri Shakhmatov 2017

[雑誌論文] Subgroups of direct products closely approximated by direct sums

M.V. Ferrer, S. Hernandez, D. Shakhmatov 2017

[雑誌論文] Selectively pseudocompact groups without non-trivial convergent sequences

D. Shakhmatov, V.H. Yanez 2017

[雑誌論文] A countable free closed non-reflexive subgroup of Z^c

M.V. Ferrer, S. Hernandez, D. Shakhmatov 2017

[学会発表] Selectively sequentially pseudocompact group topologies on abelian groups

D. Shakhmatov 2016

[雑誌論文] Direct sums and products in topological groups and vector spaces

D. Dikranjan, D. Shakhmatov, J. Spevak 2016

[学会発表] Productively Baire completeness and compactness properties

D. Shakhmatov 2016

[学会発表] Completeness properties in metric spaces and topological groups, with applications to function spaces

D. Shakhmatov 2016

[学会発表] New class of pseudocompact spaces containing all sequentially compact spaces

D. Shakhmatov 2016

[学会発表] Selective sequential pseudocompactness in topological spaces and groups

D. Shakhmatov 2016

[学会発表] Minimally alsmost periodic and connected group topologies on abelian groups

D. Shakhmatov 2015

[学会発表] 任意の可換群上面白い群位相の定めかたについて

D. Shakhmatov 2015

[雑誌論文] Topological groups with many small subgroups

D. Dikranjan, D. Shakhmatov 2015

[学会発表] Complete solution of Markov's problem on the existence of connected Hausdorff group topologies

D. Shakhmatov 2015

[学会発表] Markov's problem on the existence of connected Hausdorff group topologies on abelian groups

D. Shakhmatov 2015

[雑誌論文] A complete solution of Markov's problem on connected group topologies

D. Dikranjan, D. Shakhmatov 2015

[学会発表] Topological groups with many small subgroups

D. Shakhmatov 2015

[学会発表] Application of Hartman-Mycielski construction to two characterization problems in topological groups

D. Shakhmatov 0

[学会発表] Compact-like connected group topologies on abelian groups

D. Shakhmatov 0