Logic and Topology in Banach spaces
Logic and Topology in Banach spaces
Bilaterale Ausschreibung: Tschechien
Disciplines
Mathematics (100%)
Keywords
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Banach space,
Weak Topology,
Skeleton Of Subspaces,
Network,
Kadec-Klee property,
Amalgamation
The project is devoted to the study of topological and geometric properties of Banach spaces and their duals, aiming at a better understanding of their structure. Topological properties of the weak topology often imply important geometric properties of the Banach space in question. On the other hand, geometric properties of the Banach space often give information about its weak topology. Similar statements are true for duals of Banach spaces with the weak-star topology. We are going to explore this interplay in detail. The main project goals are: 1) Developing new tools for constructing and studying Banach spaces, using techniques from set theory and category theory. 2) Exploring different types of networks and related concepts in weak topologies, determining connections with renorming theory. Results of Goal 1 will lead to new examples, settling some of the problems concerning interplay between geometric and topological properties of non-separable Banach spaces. Goal 2 will lead to a better understanding of the weak topology and its relations to the geometric structure of a Banach space.
Logic and Topology in Banach spaces Abstract for Public Relations The project was devoted to the study of topological and geometric properties of Banach spaces and their duals, aiming at a better understanding of their structure. Topological properties of the weak topology often imply important geometric properties of the Banach space in question. On the other hand, geometric properties of the Banach space often give information about its weak topology. Similar statements are true for duals of Banach spaces with the weak -star topology. We have explored several instances of this interplay, especially implications between various convergence types of measures on boolean algebras. The main project achievements are: 1) Developing new tools for constructing and studying Banach spaces, using techniques from set theory like forcing and guessing principles. 2) Exploring different types of networks and related concepts in weak topologies, determining structural properties of Banach spaces. Results related to 1) have led to new examples, settling some of the problems concerning interplay between convergence and topological properties of non-separable Banach spaces. Results obtained in the framework of 2) have revealed the combinatorial nature of those properties, leading to better comprehension of the to pology of normed spaces.
- Universität Wien - 100%
- Jerzy Kakol, Czech Academy of Science - Czechia
- Wieslaw Kubis, Czech Academy of Science - Czechia
Research Output
- 105 Citations
- 42 Publications
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2021
Title Ideal approach to convergence in functional spaces DOI 10.48550/arxiv.2111.05049 Type Preprint Author Bardyla S -
2021
Title WAYS OF DESTRUCTION DOI 10.1017/jsl.2021.84 Type Journal Article Author Farkas B Journal The Journal of Symbolic Logic Pages 938-966 -
2022
Title On complemented copies of the space c0 in spaces Cp(X × Y) DOI 10.1007/s11856-022-2334-2 Type Journal Article Author Kakol J Journal Israel Journal of Mathematics Pages 139-177 -
2023
Title Minimally generated Boolean algebras and the Nikodym property DOI 10.1016/j.topol.2022.108298 Type Journal Article Author Sobota D Journal Topology and its Applications Pages 108298 Link Publication -
2023
Title Ideal approach to convergence in functional spaces DOI 10.1090/tran/9008 Type Journal Article Author Bardyla S Journal Transactions of the American Mathematical Society Pages 8495-8528 Link Publication -
2023
Title Grothendieck $C(K)$-spaces and the Josefson–Nissenzweig theorem DOI 10.4064/fm218-6-2023 Type Journal Article Author Kakol J Journal Fundamenta Mathematicae Pages 105-131 Link Publication -
2020
Title M-separable spaces of functions are productive in the Miller model DOI 10.1016/j.apal.2020.102806 Type Journal Article Author Repovš D Journal Annals of Pure and Applied Logic Pages 102806 Link Publication -
2020
Title A countably compact topological group with the non-countably pracompact square DOI 10.48550/arxiv.2003.03142 Type Preprint Author Bardyla S -
2023
Title On sequences of finitely supported measures related to the Josefson--Nissenzweig theorem DOI 10.48550/arxiv.2303.03809 Type Preprint Author Marciszewski W -
2019
Title The Nikodym property and cardinal characteristics of the continuum DOI 10.1016/j.apal.2018.07.003 Type Journal Article Author Sobota D Journal Annals of Pure and Applied Logic Pages 1-35 Link Publication -
2020
Title A countably compact topological group with the non-countably pracompact square DOI 10.1016/j.topol.2020.107251 Type Journal Article Author Bardyla S Journal Topology and its Applications Pages 107251 Link Publication -
2019
Title Completely Baire spaces, Menger spaces, and projective sets DOI 10.1016/j.topol.2019.02.056 Type Journal Article Author Tall F Journal Topology and its Applications Pages 26-31 Link Publication -
2019
Title Preservation of ? \gamma -spaces and covering properties of products DOI 10.1090/proc/14593 Type Journal Article Author Repovš D Journal Proceedings of the American Mathematical Society Pages 4979-4985 Link Publication -
2019
Title Convergence of measures in forcing extensions DOI 10.1007/s11856-019-1872-8 Type Journal Article Author Sobota D Journal Israel Journal of Mathematics Pages 501-529 -
2021
Title Finite powers and products of Menger sets DOI 10.4064/fm896-4-2020 Type Journal Article Author Szewczak P Journal Fundamenta Mathematicae Pages 257-275 Link Publication -
2017
Title The Nikodym property in the Sacks model DOI 10.1016/j.topol.2017.08.005 Type Journal Article Author Sobota D Journal Topology and its Applications Pages 24-34 -
2017
Title On families of subsets of natural numbers deciding the norm convergence in l 1 \ell _1 DOI 10.1090/proc/13861 Type Journal Article Author Sobota D Journal Proceedings of the American Mathematical Society Pages 1673-1680 Link Publication -
2018
Title Products of H-separable spaces in the Laver model DOI 10.1016/j.topol.2018.02.021 Type Journal Article Author Repovš D Journal Topology and its Applications Pages 115-119 Link Publication -
2018
Title Products of Menger spaces in the Miller model DOI 10.1016/j.aim.2018.06.016 Type Journal Article Author Zdomskyy L Journal Advances in Mathematics Pages 170-179 Link Publication -
2018
Title Infinite powers and Cohen reals DOI 10.4153/cmb-2017-055-x Type Journal Article Author Medini A Journal Canadian Mathematical Bulletin Pages 1-9 Link Publication -
2018
Title Families of sets related to Rosenthal’s lemma DOI 10.1007/s00153-018-0621-8 Type Journal Article Author Sobota D Journal Archive for Mathematical Logic Pages 53-69 Link Publication -
2017
Title PRODUCTS OF HUREWICZ SPACES IN THE LAVER MODEL DOI 10.1017/bsl.2017.24 Type Journal Article Author Repovš D Journal The Bulletin of Symbolic Logic Pages 324-333 Link Publication -
2019
Title Convergence of measures in forcing extensions DOI 10.48550/arxiv.1909.09387 Type Preprint Author Sobota D -
2019
Title Finite powers and products of Menger sets DOI 10.48550/arxiv.1903.03170 Type Preprint Author Szewczak P -
2019
Title Selection Principles in the Laver, Miller, and Sacks models DOI 10.48550/arxiv.1911.04480 Type Preprint Author Zdomskyy L -
2019
Title Covering properties of ?-mad families DOI 10.1007/s00153-019-00700-y Type Journal Article Author Aurichi L Journal Archive for Mathematical Logic Pages 445-452 -
2018
Title Internal characterizations of productively Lindelöf spaces DOI 10.1090/proc/14031 Type Journal Article Author Aurichi L Journal Proceedings of the American Mathematical Society Pages 3615-3626 Link Publication -
2018
Title Ways of Destruction DOI 10.48550/arxiv.1812.01480 Type Preprint Author Farkas B -
2018
Title Completely Baire spaces, Menger spaces, and projective sets DOI 10.48550/arxiv.1803.03458 Type Preprint Author Tall F -
2022
Title On complementability of $c_0$ in spaces $C(K\times L)$ DOI 10.48550/arxiv.2206.03794 Type Preprint Author Kakol J -
2022
Title On well-splitting posets DOI 10.48550/arxiv.2204.08257 Type Preprint Author Repovš D -
2022
Title On well-splitting posets DOI 10.1007/s00153-022-00818-6 Type Journal Article Author Repovš D Journal Archive for Mathematical Logic Pages 995-1005 -
2022
Title Grothendieck $C(K)$-spaces and the Josefson--Nissenzweig theorem DOI 10.48550/arxiv.2207.13990 Type Preprint Author Kakol J -
2017
Title Internal characterizations of productively Lindelöf spaces DOI 10.48550/arxiv.1704.03843 Type Preprint Author Aurichi L -
2017
Title Products of Hurewicz spaces in the Laver model DOI 10.48550/arxiv.1712.03899 Type Preprint Author Repovš D -
2017
Title Infinite powers and Cohen reals DOI 10.48550/arxiv.1705.10983 Type Preprint Author Medini A -
2022
Title On regular separable countably compact R-rigid spaces DOI 10.1007/s11856-022-2454-8 Type Journal Article Author Bardyla S Journal Israel Journal of Mathematics Pages 783-810 -
2020
Title The Josefson--Nissenzweig theorem, Grothendieck property, and finitely supported measures on compact spaces DOI 10.48550/arxiv.2009.07552 Type Preprint Author Kakol J -
2020
Title Selection principles in the Laver, Miller, and Sacks models DOI 10.1090/conm/755/15176 Type Book Chapter Author Zdomskyy L Publisher American Mathematical Society (AMS) Pages 229-242 Link Publication -
2020
Title On complemented copies of the space $c_0$ in spaces $C_p(X\times Y)$ DOI 10.48550/arxiv.2007.14723 Type Preprint Author Kakol J -
2020
Title On regular separable countably compact $\mathbb{R}$-rigid spaces DOI 10.48550/arxiv.2007.12171 Type Preprint Author Bardyla S -
0
Title Locally compact, w1-compact spaces. Type Journal Article Author Nyikos P. Journal Annals of Pure and Applied Logic, to appear Link Publication