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Grantor: Austrian Science Foundation (FWF) - Czech Science Foudation

**Objectives:**

The supreme goal of this project is to study Banach spaces of continuous and Lipschitz functions over compact spaces from the points of view of various branches of mathematics. Since every Banach space can be isometrically embedded into a Banach space of continuous functions on a compact space, such spaces constitute one of the most important classes of Banach spaces and thus their better understanding will lead to sourcing broader knowledge and comprehension of all Banach spaces in general. We propose to apply mathematical techniques and methods originating from different areas of modern analysis, geometry, topology, and logic. Such a universal approach will allow us to obtain more profound insight into the structure of Banach spaces and related objects, aiming at solving several open problems in this area. Expected results will offer new tools for studying and classifying the topology and geometry of spaces of continuous and Lipschitz functions, as well as the corresponding compact and metric spaces.

Main investigator:

IM team members:

Doležal Martin Fabian Marián Kąkol Jerzy Kostana Ziemowit |
Kurka Ondřej Maślany Natalia Müller Vladimír Russo Tommaso |

Participating institutions:

University of Innsbruck, Austria

Institute of Mathematics, Czech Academy of Sciences