. "Banach spaces and their generalizations (locally convex spaces) are one of the main tool in modern analysis. They serve as a framework for differential calculus and solving differential equations (including partial ones) and provide a great variety of questions concerning their structure. We plan to focus on topological, geometrical and algebraic structures of these spaces and interaction between these structures. The main areas include topological characterizations of important classes of Banach spaces, dual classes of compact spaces, spaces of continuous functions, properties of compact convex sets, differentiability of convex functions, relations between different weak topologies, special subsets of Banach spaces, descriptive properties of sets and operators. The nature of the project is a theoretical research in the above mentioned areas. The results will be published in scientific journals and presented at international conferences."@en . . "Banach spaces" . "0"^^ . "Banach spaces; spaces of continuous functions; weak topologies; convex sets; compact spaces; nonexpa"@en . . "1"^^ . . "1"^^ . . "The aim of this project was to better understand topological structure of Banach spaces and its relationship to geometrical, linear and algebraic structures. This aim was accomplished, the results are contained in 43 research papers, 25 out of them have"@en . . . "38"^^ . "Topological structures in functional analysis"@en . "http://www.isvav.cz/projectDetail.do?rowId=GA201/06/0018"^^ . "38"^^ . . "C\u00EDlem projektu bylo l\u00E9pe porozum\u011Bt topologick\u00E9 struktu\u0159e Banachov\u00FDch prostor\u016F a jej\u00EDmu vztahu ke geometrick\u00E9, line\u00E1rn\u00ED a algebraick\u00E9 struktu\u0159e. Tohoto c\u00EDle bylo dosa\u017Eeno, v\u00FDsledky jsou shrnuty v 43 \u010Dl\u00E1nc\u00EDch, z nich\u017E 25 ji\u017E bylo publikov\u00E1no, dal\u0161\u00EDch 10 p\u0159"@cs . . . . " spaces of continuous functions" . "2008-12-31+01:00"^^ . . . . " compact spaces" . "2008-04-25+02:00"^^ . . . "2006-01-01+01:00"^^ . "Banachovy prostory a jejich zobecn\u011Bn\u00ED (lok\u00E1ln\u011B konvexn\u00ED prostory) jsou jedn\u00EDm z hlavn\u00EDch n\u00E1stroj\u016F modern\u00ED anal\u00FDzy. Slou\u017E\u00ED jako r\u00E1mec pro diferenci\u00E1ln\u00ED po\u010Det a \u0159e\u0161en\u00ED diferenci\u00E1ln\u00EDch rovnic (v\u010Detn\u011B parci\u00E1ln\u00EDch) z\u00E1rove\u0148 poskytuj\u00ED mno\u017Estv\u00ED p\u0159irozen\u00FDch ot\u00E1zek t\u00FDkaj\u00EDc\u00ED se jejich struktury. Chceme se zam\u011B\u0159it na studium topologick\u00E9, geometrick\u00E9 a algebraick\u00E9 struktury t\u011Bchto prostor\u016F s d\u016Frazem na jejich vz\u00E1jemnou prov\u00E1zanost. K hlavn\u00EDm oblastem na\u0161eho z\u00E1jmu pat\u0159\u00ED topologick\u00E9 charakterizace d\u016Fle\u017Eit\u00FDch t\u0159\u00EDdBanachov\u00FDch prostor\u016F, du\u00E1ln\u00ED t\u0159\u00EDdy kompaktn\u00EDch prostor\u016F, prostory spojit\u00FDch funkc\u00ED, vlastnosti kompaktn\u00EDch konvexn\u00EDch mno\u017Ein, diferencovatelnost konvexn\u00EDch funkc\u00ED, vztahy mezi r\u016Fzn\u00FDmi slab\u00FDmi topologiemi, speci\u00E1ln\u00ED podmno\u017Einy Banachov\u00FDch prostor\u016F, deskriptivn\u00ED vlastnosti mno\u017Ein a oper\u00E1tor\u016F. Podstatou projektu je teoretick\u00FD v\u00FDzkum ve zm\u00EDn\u011Bn\u00FDch oblastech. V\u00FDsledky budou publikov\u00E1ny v mezin\u00E1rodn\u00EDch v\u011Bdeck\u00FDch \u010Dasopisech a prezentov\u00E1ny na mezin\u00E1rodn\u00EDch konferenc\u00EDch." . . "Topologick\u00E9 struktury ve funkcion\u00E1ln\u00ED anal\u00FDze" . . "GA201/06/0018" . "2009-10-22+02:00"^^ . " convex sets" . " weak topologies" .