# Grzegorz Plebanek

## My research

### Recent preprints

• with H. Garth Dales, Hyper-Stonean envelopes of compact spaces,
• with Witold Marciszewski, Extensions operators and twisted sums of c_0 and C(K) spaces, preprint (March 2017), see arXiv.org

### Unpublished preprint

• A normal measure on a compact connected space, preprint (2014), arXiv.org
• with David H. Fremlin, Independence--precalibers of measure algebras, preprint (2004)

### Publications since 2000 (reverse order)

1. with Antonio Aviles and Gonzalo Martinez-Cervantes, Weakly Radon-Nikodym Boolean algebras and independent sequences, Fund. Math., to appear; see arXiv.org
2. with Antonio Aviles, On disconnected images of connected spaces, Topology Appl., to appear; see arXiv.org
3. with Antonio Aviles, A Little Ado about Rectangles, Amer. Math. Monthly 124 (2017), 345–350.
4. with Antonio Aviles and Jose Rodriguez, Tukey classification of some ideals in N and the lattices of weakly compact sets in Banach spaces, Advances Math. 310 (2017), 696-758; see also arXiv.org
5. with Menachem Magidor, On properties of compacta that do not reflect in small continuous images, Topology Appl. 220 (2017), 131-139; see also arXiv.org and slides for 2016 Bedlewo conference.
6. with Piotr Drygier, Compactifications of omega and the Banach space c_0, Fund. Math. 237 (2017), 165-186; see arXiv.org
7. with Piotr Borodulin-Nadzieja, Measures on Suslinean spaces, Fund. Math. 235 (2016), 287-302; see arXiv.org
8. with S. Gabriyelyan and J. Kakol, The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces, Studia Math. 233 (2016), 110-139.
9. with Piotr Drygier, Nonseparable growth of the integers supporting a measure, Topology Appl. 191( 2015), 58-64; see also arXiv.org
10. with Damian Sobota, Countable tightness in the spaces of regular probability measures, Fund. Math. 229 (2015), 159-169; see also arXiv.org
11. with Piotr Borodulin-Nadzieja and Barnabas Farkas, Representations of ideals in Polish groups and in Banach spaces, J. Sym. Logic 80 (2015), 1268-1289, see also arXiv.org
12. On isomorphisms of Banach spaces of continuous functions, Israel J. Math.209 (2015), 1-13, see also arXiv.org
13. with Witold Marciszewski, On Borel structures in the Banach space C(\beta\omega), J. Functional Analysis 266 (2014), 4026-4036, see arXiv.org
14. with Antonio Aviles and Jose Rodriguez, A weak* separable C(K)* space whose unit ball is not weak* separable, Trans. Amer. Math.Soc. 366 (2014), 4733-4753; PDF available on request.
15. On positive embeddings of C(K) spaces, Studia Math. 216 (2013), 179-192; PDF available on request.
16. with Antonio Aviles and Jose Rodríguez, On Baire measurability in spaces of continuous functions, J. Math. Anal. Appl 398 (2013), 230-238; PDF available on request.
17. with Antonio Aviles and Jose Rodríguez, Measurability in C(2^kappa) and Kunen cardinals, Israel J. Math. 195 (2013), 1-30; see arXiv.org
18. with Witold Marciszewski, On measures on Rosenthal compacta, J. Math. Anal. Appl. 385 (2012), 185-193; PDF available on request.
19. with Mikolaj Krupski, A dichotomy for the convex spaces of probability measures , Topology Appl. 158 (2011), 2184-2190; PDF available on request
20. with Antonio Aviles and Jose Rodriguez, The McShane integral in weakly compactly generated spaces, J. Functional Analysis 259 (2010), 2776-2792; PDF available on request
21. with Witold Marciszewski, On Corson compacta and embeddings of C(K) spaces, Proc. Amer. Math. Soc. 138 (2010), 4281-4289; PDF available on request
22. with Piotr Borodulin-Nadzieja, On sequential properties of Banach spaces, spaces of measures and densities, Czechoslovak Math. J. 60 (2010), 381-399
23. with Mirna Džamonja, Strictly positive measures on Boolean algebras, J. Sym. Logic 73 (2008), 1416--1432
24. with Mirna Džamonja, On Efimov spaces and Radon measures Topology Appl. 154 (2007), 2063--2072
25. with P. Borodulin-Nadzieja, On compactness of measures on Polish spaces, , Illinois. J. Math. 49/2 (2005), 531-545
26. with Mirna Džamonja, Precalibre pairs of measure algebras, Topology Appl. 144 (2004), 67-94
27. A construction of a Banach space C(K) with few operators, Topology Appl. 143 (2004), 217--239
28. with Mirna Džamonja, Generalisations of epsilon-density, Acta Univ. Carolinae Math. Phys. 44 (2003), 57--64
29. with David H. Fremlin, Large families of mutually singular Radon measures, Bull. Pol. Acad. Sci. 51 (2003), 169--174
30. On compact spaces carrying Radon measures of large Maharam type, Acta Univ. Carolinae 43 (2002), 87--99
31. Convex Corson compacta and Radon measures, Fund. Math. 175(2002), 143-154
32. A separable perfect noncompact measure, Bull. Pol. Acad. Sci. 49 (2001), 285--289
33. A. Blass, R. Frankiewicz, C. Ryll--Nardzewski, A Note on Extensions of Asymptotic Density, Proc. Amer. Math. Soc. 129 (2001), 3313--3320.
34. with R. Frankiewicz, C. Ryll--Nardzewski, Between Lindelof property and countable tightness, Proc. Amer. Math. Soc. 129 (2001), 97--103.
35. Approximating Radon measures on first--countable compact spaces, Colloq. Math. 86 (2000), 15--23

### Slides

• Weakly compact sets in separable Banach spaces (SumTopo NY, January, 2014) slides
• A survey on small measures on compact spaces and Boolean algebras (Hejnice, January, 2014) slides
• On isomorphisms and embeddings of Banach spaces of continuous functions (Warsaw, July 2013) slides
• On isomorphisms and embeddings of C(K) spaces (Hejnice, January 2013) slides
• O przestrzeniach Banacha i algebrach Boole'a (minikonferencja dla doktorantow, pazdziernik 2012) slides
• Half-filling families of finite sets (workshop at ESSLLI in Ljubljana, 2011) slides
• Baire measurability in some C(K) spaces (Edinburgh 2011) slides.
• A dichotomy for the spaces of measures (Castro Urdiales 2011) slides.
• Baire measurability in C(2^kappa) (La Manga 2011) slides.
• Embeddings of C(K) spaces (Valencia 2010) slides.
• Banach spaces (Paseky 2008): What isomorphisms of C(K) spaces cannot forget slides.
• Winter School (Hejnice 2008): Measures, densities and some compactifications of omega slides.
• Winter School (2005): Measure precalibres slides; Short history of Wroclaw slides and appendix.