Set-theory and set-theoretical topology  Page description

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Details of project

  
Identifier
37758
Type K
Principal investigator Juhász, István
Title in Hungarian Halmazelmélet és halmazelméleti topológia
Title in English Set-theory and set-theoretical topology
Panel Mathematics and Computing Science
Department or equivalent Alfréd Rényi Institute of Mathematics
Participants Elekes, Márton
Gerlits, János
Nagy, Zsigmond
Soukup, Lajos
Szentmiklóssy, Zoltán
Starting date 2002-01-01
Closing date 2006-12-31
Funding (in million HUF) 11.357
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
\documentclass{article} \usepackage[latin2]{inputenc} \usepackage{t1enc} \usepackage[magyar]{babel} \begin{document} A pályázat keretében a legnagyobb súlyt az általános és halmazelméleti topológia terén végzett kutatások képzték. Ezek között számos már korábbban elkezdett kutatási téma mellett több új témát is sikeresen elindítottunk. Emellett -- munkatervünkkel összhangban -- foglalkoztunk inkább geometriai, ill. valós függvénytani és mértékelméleti, valamint tisztán kombinatorikai jellegű kérdésekkel is. Kiemelkedő eredményeket értünk el szétszórt kompakt terek számosságsorozatainak, topologikus terek felbonthatósági tulajdonságainak, kompakt terek halmazelméleti struktúrájának vizsgálatában. Számos megoldatlan problémát sikerült megoldani, pl. Fodor nevezetes tételének tisztán topológiai verzióját megadni. Munkánk nemzetközi elismerését jelzi, hogy a témánkban 2003 nyarán, Budapesten megrendezett konferencián olyan világhírű tudósok vettek részt, mint A. V. Arhangelszkij, A. Dow, K. Kunen, J. van Mill és a 2000. évi nemzetközi Bolyai-díjas S. Shelah. \end{document}
Results in English
\documentclass{article} \usepackage[latin2]{inputenc} \usepackage{t1enc} \begin{document} Within this project we have mainly done research work in the area of general and set-theoretic topology. In this the topics that we have dealt with included investigations that had been started earlier by us as well as several successfully launched new ones. In addition, in accordance with our research plan, we have done successful work in areas of more geometric flavor, in problems related to real analysis and measure theory, moreover concerning topics of purely combinatorial nature. We have achieved outstanding results in investigating cardinal sequences of compact scattered spaces, resolvability properties of topological spaces, and the set-theoretic structure of compact spaces. We have succeeded in solving several long-standing open problems, like e. g. finding a purely topological version of Fodor's celebrated pressing down theorem. The international recognition of our work was well-demonstrated by the fact that the topology conference that was organized in the summer of 2003 in Budapest was attended by such scientists of international fame as A. V Arhangelskii, A. Dow, K. Kunen, J. van Mill, and S. Shelah, international Bolyai prize laureate of the year 2000. \end{document}
Full text http://real.mtak.hu/342/
Decision
Yes





 

List of publications

  
Soukup L;: A lifting theorem on forcing LCS spaces, in: More sets, graphs, and numbers, Bolyai Soc. Math. Studies, no. 15, Springer, Berlin, pp. 341-358., 2006
Juhász I; Soukup L; Szentmiklóssy Z: $\mathcal D$-forced spaces: a new approach to resolvability, Top. Appl. 153 (2006), pp. 1800--1824., 2006
Juhász I; Shelah S;: Generic left-separated spaces and calibers, Top. Appl, 132 (2003), pp. 103-108, 2003
Elekes M: Hausdorff measures of different dimensions are isomorphic under the Continuum Hypothesi, Real Anal. Exchange, 30 (2004/5), pp. 605-616., 2005
Juhász I; Szymanski A;: d-calibers and d-tighness in compact spaces, közlésre elfogadva: Top. Appl. 151 (2005) pp. 66--76., 2005
Juhász I; Tkachenko M; Tkachuk V; Wilson R;: Self-transversal spaces and their discrete subspaces, Rocky Mountain J. Math. 35 (2005), pp. 1157--1172., 2005
Soukup L;: A piecewise Toronto space, Studia Sci. Math. Hung 41, no. 3, pp. 325-337., 2004
Juhász I; Shelah S; Soukup L; Szentmiklóssy Z;: Cardinal sequences and Cohen real extensions, Fund. Math., 181 (2004), no. 1, 75--88, 2004
Juhász I; van Mill J;: Almost disjoint families of connected sets, Top. Appl. 152 (2005), pp. 209--218., 2005
Juhász I; Nyikos P; Szentmiklóssy Z;: Cardinal restrictions on some homogeneous compacta, Proc. AMS, 133 (2005), pp. ~2741--2750., 2005
Gerlits, J; Juhász, I; Soukup, L; Szentmiklóssy, Z;: Characterizing continuity by preserving compactness and connectedness, Top Appl. 138 (2004), no. 1-3, 21--44, 2004
Juhász I; Szymanski A;: The topological version of Fodor\'s theorem, in: More sets, graphs, and numbers, Bolyai Soc. Math. Studies, no. 15 , pp. 157--174., 2006
Elekes M; Kunen K;: Transfinite sequences of continuous and Baire class 1 functions, Proc. Amer. Math. Soc. 131 (2003), no. 8, 2453--2457, 2003
Gerlits J; Sági G;: Ultratopologies, Math. Log. Quart. Vol. 50 No. 6, pp. 603-612 (2004), 2004
Elekes M; Steprans J;: Less than $2^\omega$ many translates of a compact nullset may cover the real line, Fund. Math. 181 (2004), no. 1, 89--96, 2004
Elekes M: Measurable envelopes, Hausdorff measures and Sierpinski sets, Coll. Math. 98 (2003), no.~2, 155--162., 2003
Elekes M; Keleti T: Borel sets which are null or non-$\sigma$-finite for every translation invariant measure, Adv. Math. 201; no. 1; pp. 102-115., 2006
Elekes M; Steprans J: Chains of Baire class 1 functions and various notions of special trees, Israel J. Math 151, pp. 179-187., 2006
Juhász I; Weiss W;: Cardinal sequences, Ann. Pure Appl. Logic 144 (2006), pp. 96--106., 2006
Juhász I; Szentmiklóssy Z: Discrete subspaces of countably tight compacta, Ann. Pure Appl. Logic 140, pp. 72-74., 2006
Elekes M. Tóth Á.,: Covering locally compact groups by less than continuum many translates of a compact nullset, Fund. Math., megjelenés alatt, 2006
Gerlits J; Juhász I; Szentmiklóssy Z: Two improvements on Tka\v cenko's addition theorem, CMUC, 46 (2005), pp. ~705--710., 2005
Erdős P; Soukup L;: How to split antichains in infinite posets, Journal of Combinatorial Theory, Ser. B, közlésre elfogadva, 2007
Abraham U; Gorelic I; Juhász I;: On Jakovlev spaces, Israel J. Math. 152 (2006), pp. 205--219., 2006
Juhász I; van Mill J;: Covering compacta by discrete subspaces, Top. Appl. 154 (2007), pp. 283--286., 2007
I.~Juh{\'a}sz, L.~Soukup and Z.~Szentmikl{\'o}ssy}: Resolvability of spaces of small spread or extent, Top. Appl. 154 (2007), pp. 144--154., 2007
Juhász I; Soukup L; Weiss W;: Cardinal sequences of length $< \omega_2$ under GCH, Fund. Math. 189 (2006), pp. 35--52., 2006
Juhász I; Szentmiklóssy Z; Szymanski A;: Eberlein compacts of finite metrizability number, közlésre elfogadva: CMUC, 2007
Juhász I; Weiss W;: Good, splendid, and Jakovlev, in: Open problems in Topology, Nort-Holland Publ. Co.; közlésre elfogadva, 2007



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