Set-theoretic topology  Page description

Help  Print 
Back »

 

Details of project

 
Identifier
61600
Type K
Principal investigator Juhász, István
Title in Hungarian Halmazelméleti topológia
Title in English Set-theoretic topology
Keywords in Hungarian topologikus terek, számosságfüggvények
Keywords in English topological spaces, cardinal functions
Discipline
Mathematics (Council of Physical Sciences)100 %
Panel Mathematics and Computing Science
Department or equivalent Alfréd Rényi Institute of Mathematics
Participants Elekes, Márton
Gerlits, János
Hajnal, András
Mátrai, Tamás
Nagy, Zsigmond
Soukup, Lajos
Szentmiklóssy, Zoltán
Starting date 2006-03-01
Closing date 2010-06-30
Funding (in million HUF) 16.640
FTE (full time equivalent) 11.58
state closed project
Summary in Hungarian
\usepackage[latin2]{inputenc}


\begin{document}

A 60-as évek második fele óta folyamatos és intenzív kutatómunka
folyik Hajnal András és Juhász István vezetésével Budapesten a
halmazelméleti topológia területén. Ennek a munkának nemzetközi
elismertségét bizonyítja pl. az a tény, hogy a témában 2003-ban
Budapesten megrendezett konferencián olyan világhírű tudósok vettek
részt, mint A. V. Arhangelszkij, A. Dow, K. Kunen, J. van Mill és S.
Shelah. Pályázatunknak éppen az a célja, hogy ezeket a sikeres
kutatásokat tovább folytassuk, természetesen kitejesztve őket új
irányokba is, mint pl. a leíró halmazelmélet, valós függvénytan és
mértékelmélet.

A pályázat elnyerése lehetővé tenné számunkra, hogy kiterjedt
nemzetközi kapcsolatainkat fenntartsuk, sőt a lehetőségekhez mérten
kibővitsük, továbbá hogy az eredményes kutatások folytatásához
szükséges technikai és egyéb felté-\\teteleket biztosítsuk.

\end{document}
Summary
\documentclass{article}
\usepackage[magyar]{babel}
\usepackage{amssymb}
\usepackage[latin2]{inputenc}

\begin{document}
Since the second half of the sixties an intensive and uninterrupted
research work has been carried out by our group in Budapest in the
area of set-theoretic topology, under the leadership of András
Hajnal and István Juhász. The international recognition of this work
is well-demonstrated by the fact that the conference that was
organized in this area in Budapest in 2003 was attended by such
scientists of international fame as A. V. Arhangelszkij, A. Dow, K.
Kunen, J. van Mill and S. Shelah. The exact aim of this project is
to carry on this successful research work and, of course, extend it
to new directions like descriptive set-theory, theory of real
functions, and measure-theory.

Getting this grant would enable us to keep up, and possibly even
extend, our wide ranging international relations in the area of
set-theoretic topology. Also, it would make it possible for us to
insure the technical and other types of conditions necessary for
carrying on our successful research work.

\end{document}





 

Final report

 
Results in Hungarian
Ebben az OTKA-pályázatban -- kutatási tervünknek megfelelően -- kutatásokat végeztünk és jelentős eredményeket értünk el a következő négy területen: (I) Halmazelméleti topológia (kompakt terek, szétszórt terek, számosságfüggvények, felbonthatóság) (II) Leíró halmazelmélet (III) Végtelen és véges kombinatorika (IV) Valós analízis és mértékelmélet . Eredményeinket 45 dolgozatban írtuk le, amelyek túlnyomó többsége a megfelelő terület legrangosabb nemzetközi folyóirataiban jelentek meg, illetve fognak megjelenni (ezek közül 6 dolgozatot már benyujtottunk, de eddig még nem lettek elfogadva). Kutatócsoportunk 8 résztvevővel indult, de sajnos egyikünk -- Gerlits János) 2008-bqn elhunyt. Kutatási eredményeinkről számos nemzetközi konferencián is számot adtunk, sok esetben közülünk négyen (Elekes, Juhász, Mátrai, Soukup) mint plenáris és/vagy meghívott előadó.
Results in English
In the present project, following our research plan, we have done research and established a number of significant results in the following four areas: (I) Set-theoretic topology (compact spaces, scattered spaces, cardinal functions, resolvability) (II) Descriptive set-theory (III) Infinite and finite combinatorics (IV) Real analysis and measure theory We presented our results in 45 papers almost all of which appeared or will appear in the leading international journals of these fields (6 of these papers have been submitted but not accepted as yet). Our research group consisted of 8 people, one of us -- J. Gerlits -- unfortunately passed away in 2008. We also participated at a large number of international conferences, four of us (Elekes, Juhász, Mátrai, Soukup) as plenary and/or invited speakers at many of these.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=61600
Decision
Yes





 

List of publications

 
Soukup, Lajos: Elementary submodels in infinite combinatorics,, Discrete Math., submitted, 2010
Soukup, Lajos: Pcf theory and cardinal invariants of the reals,, CMUC., submitted, 2010
Mátrai T: More cofinal types of definable directed orders, Trans. Amer. Math. Soc.; submitted, 2010
Mátrai T: Infinite dimensional perfect set theorems, Trans. Amer. Math. Soc.; submitted, 2010
Juhász I; Szentmiklóssy Z: A strengthening of the Cech - Pospisil theorem, Top. Appl.; 155, 17-18. , 2102--2104., 2008
Juhász I; Soukup L; Szentmiklóssy Z: Resolvability and monotone normality, Israel J. Math.; 166 , 1–-16., 2008
Juhász I; Szentmiklóssy Z: On $d$-separarability of powers and $C_p(X)$, Top. Appl.; 155 (2008), no. 4, 277--281., 2008
Juhász I; Shelah S: Hereditarily Lindelöf spaces of singular density, Studia Sci. Math. Hung.; 45, 4 , 557-562, 2008
Soukup L: Nagata's conjecture and countably compactifications, Topology Appl. 155 , no. 4, 347-353., 2008
Erdős P; Soukup, L;: Quasi-kernels and quasi-sinks in infinite graphs, Journal of Combinatorial Theory, Series B; Discrete Math. 309(10), volume 309, 3040–3048, 2009
Elekes M; Laczkovich M: A cardinal number connected to the solvability of systems of difference equations in a given function class, J. Anal. Math.; 101, 199-218., 2007
Mátrai; T: Hurewicz test sets for generalized separation and reduction, Math. Proc. Cambridge Phil. Soc.; 143 , No. 2, 407-417, 2007
Mátrai; T: Topological aspects of Hurewicz tests for the difference hierarchy, Ukrainian Mathematical Bulletin; 3 , no. 4, 520-546., 2006
Juhász I; Vaughan J: Countably compact hyperspaces and Frolik sums, Top. Appl.; 154, 2434--2448, 2007
Juhász I; Shelah S; Soukup L: Resolvability vs. almost resolvability, Top. Appl.; 156, no. 11, 1966--1969, 2009
Juhász I; Soukup L; Szentmiklóssy Z: First countable spaces with no point-countable \pi-bases, Fund. Math.; 196 , no. 2, 139--149., 2007
Juhász I; Szentmiklóssy Z: Projective \pi-character bounds the order of a \pi-base, Proc. Amer. Math. Soc.; 136, 2979-2984, 2008
Gorelic I; Juhász I: AB-compacta, Comm. Math Univ. Carol..; 49, 1, 2008
Balka R; Elekes M: The structure of rigid functions, J. Math. Anal. Appl.; 345 , no. 2, 880-888., 2008
Elekes M; Máthé A: Can we assign the Borel hulls in a monotone way?, Fund. Math.; 205 no. 2, 105-115., 2009
Soukup L: Infinite Combinatorics: From Finite to Infinite, Horizons of Combinatorics, Bolyai Society Mathematical Studies. vol 17,pp 189-213., 2008
Elekes M; Keleti T; Máthé A: Self-similar and self-affine sets; measure of the intersection of two copies, Ergod. Th. & Dynam. Sys. 30, no. 2, 399–440., 2010
Mátrai; T: Covering $\Sigma^{0}_{\xi}$-generated ideals by $\Pi^{0}_{\xi}$ sets, Comm. Math. Univ. Carol. 48 , no. 2, 245-268., 2007
Elekes M; Mátrai T; Soukup L: On splitting infinite-fold covers, Fund. Math., to appear, 2009
Mátrai T; Zeleny M;: On monotone presentations of Borel sets, Real Anal. Exchange; 34 no. 2, 311--318, 2009
Mátrai T: Kenilworth, Proc. Amer. Math. Soc.; 137, 1115-1125., 2009
Mátrai T: \Pi^0_2-generated ideals are unwitnessable, Real Anal.\ Exchange; közlésre benyujtva, 2009
Fuchino S; Juhász I; Soukup L; Szentmiklóssy Z; Usuba T: Fodor-type reflection principle, Top. Appl., 157 , no. 8, pp. 1415--1429, 2010
Mátrai T: On a new $\sigma$-ideal of compact sets, Top. Appl.; 157; no. 2, 1479--1484, 2010
Erdős P L; Soukup L;: No finite-infinite antichain duality in the homomorphism poset D of directed graphs, Order, 1-9, 2010
Farkas B; Soukup L: More on cardinal invariants of analytic P-ideals, Comment. Math. Univ. Carolin. 50 (2), 281–295., 2009
Martinez J-C; Soukup L;: Universal locally compact scattered spaces, Topology Proc. 35, volume 35, 19–36, 2010
Martinez J-C, Soukup L;: The D-property on unions of scattered spaces, Top. Appl. 156(18), 3086–3090, 2009
Juhász I; Koszmider P; Soukup L;: A first countable, initially omega_1-compact but non-compact space, Top. Appl., 156 , no. 10, 1863--1879., 2009
Balka R; Elekes M;: The structure of continuous rigid functions of two variables, Real Anal. Exch. ; közlésre benyújtva, 2009
Juhász I; Szentmiklóssy Z;: Interpolation of $\kappa$-compactness and PCF theory, CMUC, 50, 2 , 315--320, 2009
Juhász I; Weiss W;: On the convergence and character spectra of compact spaces, Fund. Math., 207, pp. 179--196, 2010
Dzamonja M; Juhász I: CH, a problem of Rolewicz, and bidiscrete systems, Top. Appl., megj. alatt, 2010
Hajnal A; Juhász I; Soukup L; Szentmiklóssy Z: Conflict-free colorings of (strongly) almost disjoint set-systems, Acta Math. Hung., to appear, 2010
Martinez, Juan Carlos, and Soukup, Lajo: Superatomic Boolean algebras constructed from strongly unbounded functions,, Mathematical Logic Quarterly, submitted, 2010
Martinez, Juan Carlos, and Soukup, Lajo: Cardinal sequences of LCS spaces under GCH,, Ann. Pure Appl. Logic 161, volume 161, 1180–1193, 2010
Soukup, Lajos: Wide scattered spaces and morasses, Topology Appl., submitted, 2010
Soukup, Lajos: Indestructible colourings and rainbow Ramsey theorems,, Fund. Math. 202(2), volume 202, 161–180, 2009
Duffus, Dwight, Erdős, Péter L., Nešetril, J., and Soukup, Lajos: Antichains in the homomorphism order of graphs, Comment. Math. Univ. Carolin. 48(4), volume 48, 571–583, 2007
Erdős, Peter L., Stoyle, Jens, and Soukup, Lajos:: Balanced Vertices in Trees and a Simpler Algorithm to Compute the Genomic Distance,, Appl. Math. Letters, to appear, 2010




Back »