. . . . "39"^^ . . "Among the best results belong the proof of equivalence between J.von Neumann problem and D. Maharam problem from measure theory. Also results about embedding of function spaces in to Banach spaces, on generation of all topological spaces by products and"@en . "39"^^ . "1"^^ . . "Neuvedeno."@en . "Mezi nejv\u011Bt\u0161\u00ED \u00FAsp\u011Bchy pat\u0159\u00ED d\u016Fkaz ekvivalence probl\u00E9mu J.von Neumanna s probl\u00E9mem teorie m\u00EDry D. Maharamov\u00E9. Dal\u0161\u00EDmi hodnotn\u00FDmi v\u00FDsledky jsou Pelantova tvrzen\u00ED o vno\u0159en\u00ED funk\u010Dn\u00EDch prostor\u016F do Banachov\u00FDch prostor\u016F, pr\u00E1ce o generov\u00E1n\u00ED v\u0161ech topologick\u00FDch p"@cs . . "2"^^ . . . . "http://www.isvav.cz/projectDetail.do?rowId=GA201/03/0933"^^ . "Researchers will try to solve some difficult problems in fields of pure mathematics concerning set-theoretical topology, topological algebraic structures and category theory. We will concentrate mainly at: structural properties of filters, ideals,independent families and almost disjoint systems; Borel and projective hierarchy in both topological and logical setting; topological aspects of functional analysis with emphasis on compactness; theory of topological hyperspaces as a technical tool and asubject for research; properties of topological groups and other algebraic structures equipped with topology; topological methods in computer science. Main techniques, which will be used and developed during the research project, are: combinatorial andcategorial approach, connections to Boolean algebras with emphasis on forcing, connections to measure theory and to functional analysis. The project proposal unites three generations of researchers working in fields mentioned above."@en . . "0"^^ . . . . . "Mno\u017Einov\u011B teoretick\u00E9 a kategori\u00E1ln\u00ED metody v topologick\u00FDch a algebraick\u00FDch struktur\u00E1ch" . "Set-theoretical and categorial methods in topological and algebraic structures"@en . . . . . "\u0158e\u0161itel\u00E9 se pokus\u00ED vy\u0159e\u0161it n\u011Bkter\u00E9 obt\u00ED\u017En\u00E9 probl\u00E9my z\u00A0oblast\u00ED \u010Dist\u00E9 matematiky, t\u00FDkaj\u00EDc\u00ED se mno\u017Einov\u011B-teoretick\u00E9 topologie, topologicko-algebraick\u00FDch struktur a teorie kategori\u00ED. Hlavn\u011B se soust\u0159ed\u00EDme na: struktur\u00E1ln\u00ED vlastnosti filtr\u016F, ide\u00E1l\u016F,nez\u00E1visl\u00FDch soubor\u016F a skorodisjuntn\u00EDch syst\u00E9m\u016F; borelovskou a projektivn\u00ED hierarchii jak v\u00A0topologick\u00E9m, tak logick\u00E9m kontextu; topologick\u00E9 aspekty funkcion\u00E1ln\u00ED anal\u00FDzy s\u00A0d\u016Frazem na kompaktnost; teorii topologick\u00FDch hyperprostor\u016F jako technick\u00FDprost\u0159edek a jako p\u0159edm\u011Bt v\u00FDzkumu; vlastnosti topologick\u00FDch grup a dal\u0161\u00EDch algebraick\u00FDch struktur opat\u0159en\u00FDch topologi\u00ED; topologick\u00E9 metody v\u00A0informatice. Hlavn\u00ED techniky, kter\u00E9 se budou pou\u017E\u00EDvat a rozv\u00EDjet b\u011Bhem pr\u00E1ce na projektu, jsou: kombinatorick\u00E9 akategori\u00E1ln\u00ED metody, souvislosti s\u00A0Booleov\u00FDmi algebrami s\u00A0d\u016Frazem na forsing, souvislosti s\u00A0teori\u00ED m\u00EDry a funkcion\u00E1ln\u00ED anal\u00FDzou. Grantov\u00FD n\u00E1vrh spojuje t\u0159i generace pracovn\u00EDk\u016F, \u010Dinn\u00FDch ve\u00A0v\u00FD\u0161e zm\u00EDn\u011Bn\u00FDch oblastech v\u00FDzkumu." . "2009-01-15+01:00"^^ . "GA201/03/0933" .