1. 1.H. Michalewski, R. Pol, On a Hurewicz-Type Theorem and a Selection Theorem of Michael, 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. 2.H. Michalewski, Game-Theoretic Approach to the Hereditary Baire Property of C_p(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. 3.H. Michalewski, 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. 4.H. Michalewski, 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. 5.A. Krawczyk, H. Michalewski An example of a topological group, 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. 6.A. Krawczyk, H. Michalewski, Linear metric spaces close to being sigma-compact, preprint of the Institute of Mathematics of the University of Warsaw. 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. 7.H. Michalewski, 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. 8.A. Komisarski, H. Michalewski, P. Milewski, Functions Equivalent to Borel Measurable Ones, Bull. Pol. Acad. Sci. 58, 2010, 55-64. Using a recent result of J. Saint Raymond 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. 9.A. Komisarski, H. Michalewski, P. Milewski, Bourgain-Fremlin-Talagrand Dichotomy and dynamical systems. 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. 10. W. Kubis, H. Michalewski, Small Valdivia compact spaces, Topology and its Applications 153 (2006),  2560–2573.  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.
    

11. 11.M. Kojman, H. Michalewski, Borel Extensions of Baire Measures in ZFC. Fund. Math. 211 (2011), 197-223. We prove that every Baire measure on the Kojman-Shelah Dowker space admits a Borel extension. If the continuum is not a real-valued measurable cardinal then every Baire measure on the M.~E. Rudin Dowker space admits a Borel extension, submitted.
    

12. 12.A. Krawczyk, W. Marciszewski, H. Michalewski, Remarks on the set of G_delta-points in Eberlein and Corson Compact Spaces. Topology and its Applications 156 (2009),  1746-1748. We show that, for every scattered Eberlein compact space K, the set of points with countable base of neighborhoods in K is a G_\delta -set in K. We also give an example of a scattered Eberlein compactum with non-metrizable set of points with countable base of neighborhoods in K. Moreover, we give an example of a Corson compact  space K such that the set f points with countable base of neighborhoods in K does not contain any dense G_\delta subset of K, preprint.
    

13. 13.Sz. Hummel, H. Michalewski, D. Niwiński, On the Borel inseparability of game tree languages. STACS 2009, 565-575. We give an example of a pair of Borel inseparable coanalytic sets and show implications of inseparability in the context of automata on trees, accepted for STACS 2009.
    

14. 14. H. Michalewski, D. Niwiński, On separation question for tree languages. Submitted. We give an example of a pair of regular (1,3)-languages not separable by a Sigma^1_1-inductive set.
    

Other Materials:

MA Thesis (1998), Przestrzenie funkcji ciaglych i przestrzenie dziedzicznie Baire'a (in Polish; Function spaces and hereditary Baire spaces). Supervised by Witold Marciszewski.

PhD Thesis (2002) Przestrzenie funkcyjne z topologia zbieznosci punktowej (in Polish; Function spaces with topology of pointwise convergence). Supervised by Witold Marciszewski.