On a plane compactum with the maximal shape
On a problem of L. Mišík
On a problem of Lelek concerning open mappings
On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim)
On a question of Borsuk concerning non-continuous retracts II
On a question of Borsuk concerning non-continuous retracts I
On a question of
In this short article we answer the question posed in Ghadermazi M., Karamzadeh O.A.S., Namdari M., On the functionally countable subalgebra of , Rend. Sem. Mat. Univ. Padova 129 (2013), 47–69. It is shown that is isomorphic to some ring of continuous functions if and only if is functionally countable. For a strongly zero-dimensional space , this is equivalent to say that is functionally countable. Hence for every -space it is equivalent to pseudo--compactness.
On a question of E.A. Michael
A negative answer to a question of E.A. Michael is given: A convex -subset of a Hilbert space is constructed together with a l.s.c. map having closed convex values and no continuous selection.
On a result of Adasch and Ernst.
On a selection theorem of Blum and Swaminathan
Blum and Swaminathan [Pacific J. Math. 93 (1981), 251–260] introduced the notion of -fixedness for set-valued mappings, and characterized realcompactness by means of continuous selections for Tychonoff spaces of non-measurable cardinal. Using their method, we obtain another characterization of realcompactness, but without any cardinal assumption. We also characterize Dieudonné completeness and Lindelöf property in similar formulations.
On a shadowing lemma in metric spaces
In the present paper conditions are studied, under which a pseudo-orbit of a continuous map , where is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map .
On a simultaneous selection theorem
Valov proved a general version of Arvanitakis's simultaneous selection theorem which is a common generalization of both Michael's selection theorem and Dugundji's extension theorem. We show that Valov's theorem can be extended by applying an argument by means of Pettis integrals due to Repovš, Semenov and Shchepin.
On a stability theorem for the fixed-point property
On a theorem of Holický and Zelený concerning Borel maps without -compact fibers
The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.
On a theorem of P. S. Aleksandrov
On a theorem of Popa and Noiri on multifunctions
On a theorem of van Douwen.
On a theorem of W.W. Comfort and K.A. Ross
A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is -embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group and prove that every -dense subspace of a topological group , such...
On a Variant of the Gagliardo-Nirenberg Inequality Deduced from the Hardy Inequality
We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.
On a weak form of weak quasi-continuity.