I am a topologist and I work at the Institute of Mathematics, University of Warsaw. Currently, between September 2005 and September 2006, I am a postdoc at Ben Gurion University in Israel. Between 1998 and 2002 I studied as a PhD student under supervision of Witold Marciszewski. Here is a picture (52kB) from Toposym 2001, which shows my supervisor and me.

Information on Scientific Research

• Research Interest: general topology, set theory, abstract functional analysis (click here for a postscript file with details).
• Curriculum Vitae: postscript file and PDF file.

Master thesis: Przestrzenie funkcji ciaglych i przestrzenie dziedzicznie Baire'a (in Polish; Function spaces and hereditary Baire spaces). Supervised by Witold Marciszewski. Defended in 1998.

Doctoral thesis: Przestrzenie funkcyjne z topologia zbieznosci punktowej (in Polish; Function spaces with topology of pointwise convergence). Supervised by Witold Marciszewski. Given to the referees on March 15th 2002 ( postscript file with my thesis ). Defended January 9th 2003.

Publications [a part of them downloadable in the form of postscript files]

1. On a Hurewicz-type theorem and a selection theorem of Michael, joint paper with Roman Pol, Bull. Pol. Acad. Sci. 43 (1996), 273-275.
   We proved a generalization of Kechris-Louveau-Woodin theorem via an application of a theorem of Michael on selections.
2. Game--theoretic approach to the hereditary Baire property of $C_p({\mathbb N}_F)$, Bull. Pol. Acad. Sci. 46 (1998), 135-140.
   I gave a characterization in terms of topological games of these countable spaces $X$ with one non--isolated point, such that the function space $C_p(X)$ is a hereditary Baire space (every closed subset satisfies the Baire Category Theorem). It is a part of my master degree thesis.
3. Homogeneity of K(Q), Tsukuba Journ. of Math. 24 (2000), 297--302.
   I proved that all separable, metrizable, zero--dimensional spaces which are of the first category in itself and which are locally coanalytic complete, are homeomorphic. As a corollory I proved that the space of all compact subspaces of rationals, endowed with Hausdorff metric, is a topological group.
4. An answer to a question of Arkhangelskii, Comment. Math. Univ. Carolinae 42 (2001)
   I gave two examples of a space with the property that the spaces $C_p(X)$ and $C_p(X\times\omega)$ are linear homeomorphic, but the spaces $C_p(X)$ and $C_p(X\times(\omega+1))$ are not linear homeomorphic, where $\omega$ and $\omega+1$ are countable ordinals equiped with ordinal topology. One of the examples is a metrizable space (it is so called the Stone space ).
5. An example of a topological group, joint work with Adam Krawczyk, Topology and its Applications 127 (2003), pp.325-330.
   We consider notions of o-boundedness and strong o-boundedness, introduced by Tkachenko and Okunev, which generalize the notion of $\sigma$-compactness in the class of topological groups. We gave an example of a topological group which is a Lindelof P-space, but which is not strongly o-bounded.
6. Linear metric spaces close to being $\sigma$--compact, joint work with Adam Krawczyk.
   We shown, under an additional set theorethical assumption implied by MA, an example of two o-bounded, metrizable, separable topological groups, such that their product is not o-bounded. This construction appeals to the affinity between the o-bounded property and Menger property of a given topological group.
7. On condensations of projective sets onto compacta, Proc. Amer. Math. Soc. 131 (2003) no. 11, pp.3601-3606.
   I proved that every coanalytic-complete, separable, metrizable space might be bijectively, continuously mapped onto the Hilbert cube. As a corollary I noticed that the space $C_p(A)$ admits a weaker compact topology if $A$ is an analytic, separable, metrizable space. For sigma-compact $A$ this result was proved earlier by Arkhangelskii.
8. Functions equivalent to Borel measurable ones, joint work with Andrzej Komisarski and Pawel Milewski.
   Under additional assumption of Analytic Determinacy we gave some conditions on a given function $f:R->R$ ($R$ stands for the real line), which are necessary and sufficient for existence of a Borel-measurable function equivalent, in a sense defined by Ryll-Nardzewski and Morayne, to the function $f$.
9. Bourgain-Fremlin-Talagrand Dichotomy and dynamical systems , joint work with Andrzej Komisarski and Pawel Milewski.
   For a given continuous function $f:[0,1]\to [0,1]$ we give a necessary and sufficient condition that the closure of subsequent iterations $f^n$ (n - natural number) in the Tychonoff cub $[0,1]^[0,1]$ is metrizable. It gives an answer to a question of Gilles Godefroy from 2002. Our reasoning appeared to be a re-discovery of a result of Angela Koehler from 1994.
10. Small Valdivia compact space, joint work with Wieslaw Kubis, accepted to Top.Appl.
    Under certain conditions we show that retractions and open images of Valdivia compact spaces remain Valdivia. In general, as was proved by Kubis and Uspeinski, open image of a Valdivia compact space may be not Valdivia.

The Summer School in Szumin!

Zajecia z analizy funkcjonalnej 2004/2005

Zajecia z analizy matematycznej 2004/2005

Program seminarium Zakladu Topologii