Selected publications

Papers and conference reports

  1. (with Michael Hrusak, Tamas Matrai, Ales Nekvinda and Vaclav Vlasak) Properties of functions with monotone graphs. Submitted. (pdf)
  2. Small sets of reals through the prism of fractal dimensions. Submitted. (pdf)
  3. Packing measures and dimensions on cartesian products. Publicacions Matematiques, to appear. (pdf)
  4. (with Tamás Keleti and András Máthé) Hausdorff dimension of metric spaces and Lipschitz maps onto cubes. International Mathematics Research Notices, to appear. (pdf)
  5. (with Petr Simon and Michael Hrusak) Weak partition properties on trees. Archive for Mathematical Logic, to appear. (pdf)
  6. Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps. Fundamenta Mathematicae 218(2012). (pdf)
  7. (with Michael Hrusak) Cardinal invariants of monotone and porous sets. Journal of Symbolic Logic 2012. (pdf)
  8. (with Ales Nekvinda) Monotone metric spaces. Order 2012. (pdf)
  9. (with Ales Nekvinda) A Cantor set in the plane that is not sigma-monotone. Fundamenta Mathematicae 213 (2011). (pdf)
  10. Packing measures and cartesian products. Real Analysis Exchange 2008/9. (pdf)
  11. Hausdorff dimension of X x X. Real Anal. Exchange 2006, 30th Summer Symposium Conference, p. 99.
  12. How many translates of a small set are needed to cover the line? Real Anal. Exchange 2005, 29th Summer Symposium Conference, p. 39-43.
  13. Polar sets and Hausdorff dimension in nonseparable spaces? Real Anal. Exchange 2004, 28th Summer Symposium Conference, p. 63-67.
  14. Small opaque sets. Real Anal. Exchange 28 (2002/03), no. 2, 455-469.
  15. Hentschel-Procaccia spectra in separable metric spaces. Summer Symposium in Real Analysis XXVI. Real Anal. Exchange 2002, 26th Summer Symposium Conference, p. 115-119.
  16. (with Piotr Zakrzewski) Measures in locally compact groups are carried by meager sets. Journal of Applied Analysis 7 (2001), no. 2, p. 225-233.
  17. A set that is fat and slim at the same time. Summer Symposium In Real Analysis XXIV, Denton 2000. Real Analysis Exchange (2001).
  18. Dimension zero vs. measure zero. Proc. Amer. Math. Soc. 128 (2000), no. 6, p. 1769-1778.
  19. Residual measures in locally compact spaces. Topology Appl. 108 (2000), no. 3, p. 253-265.
  20. Multifractal spectra that are not spectra. Real Analysis Exchange 25 (2000), no. 1, p. 13-14
  21. (with Jozef Bobok) Topological entropy on zero-dimensional spaces. Fund. Math. 162 (1999), no. 3, p. 233-249.
  22. Killing residual measures. Journal of Applied Analysis 5 (1999), no. 2, p. 223-238.
  23. A nowhere dense set is deeply nowhere dense. Questions and Answers in General Topology 17 (1999), no. 1, p. 89-90.
  24. Yet a shorter proof of an inequality of Cutler and Olsen. Real Analysis Exchange 24 (1998/99), no. 2, p. 873-874.
  25. Locally small measures are uniformly small. Collection of papers, Czech Technical University, Prague, 1998, p. 87-92.
  26. A note on the Ramsey-type theorem of Erdos. Comment. Math. Univ. Carol. 31 (1990), no. 4, p. 765-767.

Preprints and unpublished notes

  1. Universal measure zero sets with full Hausdorff dimension. (pdf)
  2. Additivity and pathology of Hasdorff measures. (pdf)
  3. Extending a metric over a Gδ-set. (pdf)
  4. Hentschel-Procaccia spectra in separable metric spaces. (pdf)
  5. Measures in metric spaces are carried by meager sets. (pdf)

Conference and other presentations

  1. Applications of monotone spaces theory: Peano curves, Urbanski conjecture, differentiability. . .. Stara Lesna 2012.
  2. Meager-additive sets through the prism of fractal dimension. Budapest 2011.
  3. Translates of compact sets and combinatorics of fractal dimensions. Prague 2011.
  4. Fractal dimensions vs. small sets of reals. Chicago 2008.
  5. Packing measures and cartesian products. Oxford 2007.
  6. Packing dimensions and cartesian products. St Andrews 2007.

Textbooks

  1. Matematika 3. Czech Technical University, Prague, 2007, 155 pages, in Czech.
  2. (with F. Bubeník) Matematika 1. Czech Technical University, Prague, 2005, 159 pages, in Czech.
  3. Funkce více proměnných. Department of Mathematics, Czech Technical University, Prague, 2004, 27 pages, in Czech.
  4. Vektorová pole. Czech Technical University, Prague, 1999, 72 pages, in Czech, ISBN 80-01-02075-4.