19 citations · 35 across the 22 of their papers we have counts for
24 papers
On condensations of spaces onto Banach spaces with the weak topology
Mikołaj Krupski, Witold Marciszewski
We show that for a broad class of spaces , the space of continuous real-valued functions on equipped with the pointwise topology maps bijectively onto any separable…
On the -invariance of the hereditary Baire property and related results
Mikołaj Krupski, Kacper Kucharski
We prove that if and are first-countable perfect spaces such that the free Abelian topological groups and are topologically isomorphic, then is a heredita…
The Cartesian product of any family of -spaces is -Fréchet-Urysohn
Mikołaj Krupski, Kacper Kucharski
In this note, we prove that an arbitrary product of -spaces is a -Fréchet-Urysohn space. We also show that the boundary tightness of a product is at most pro…
Bounded uniform homeomorphisms between -spaces preserve pseudocompactness
Mikolaj Krupski, Vesko Valov
For any Tychonoff space let (resp., ) be the set of all continuous (resp., and bounded) functions on with the pointwise convergence topology. Given Tycho…
Lindelöf scattered -spaces are -compact
Mikołaj Krupski
We show that every Lindelöf scattered -space is -compact. This result generalizes a theorem proved recently by Avilés and the author in [Topology Appl. 363 (2025), Paper No.…
Every Lindelöf scattered subspace of a -product of real lines is -compact
Antonio Avilés, Mikołaj Krupski
We prove that every Lindelöf scattered subspace of a -product of first-countable spaces is -compact. In particular, we obtain the result stated in the title. This answers som…
Characterizing function spaces which have the property (B) of Banakh
Mikołaj Krupski, Kacper Kucharski, Witold Marciszewski
A topological space has the property (B) of Banakh if there is a countable family of closed nowhere dense subsets of absorbing all compact subsets…
On the class of NY compact spaces of finitely supported elements and related classes
Antonio Avilés, Mikołaj Krupski
We prove that a compact space embeds into a -product of compact metrizable spaces (-product of intervals) if and only if is (strongly countable-dimensional) hereditar…
Some examples concerning and metrizably fibered compacta
Antonio Avilés, Mikołaj Krupski
The class of -spaces was introduced in 2006 by Kubiś, Okunev and Szeptycki as a natural refinement of the classical and important notion of Lindelöf -spaces. Compact…
Some remarks on the projective properties of Menger and Hurewicz
Mikołaj Krupski, Kacper Kucharski
It is known that both the Menger and Hurewicz property of a Tychonoff space can be described by the way is placed in its Čech-Stone compactification . We provide analog…
On -pseudocompactess and uniform homeomorphisms of function spaces
Mikołaj Krupski
A Tychonoff space is called -pseudocompact if for every continuous mapping of into the image is compact. This notion generalizes pseudocompactn…
Linear homeomorphisms of function spaces and the position of a space in its compactification
Mikołaj Krupski
An old question of A.V. Arhangel'skii asks if the Menger property of a Tychonoff space is preserved by homeomorphisms of its function space . We provide affirmative ans…
Games and hereditary Baireness in hyperspaces and spaces of probability measures
Mikołaj Krupski
We establish that the existence of a winning strategy in certain topological games, closely related to a strong game of Choquet, played in a topological space and its hyperspac…
A countable dense homogeneous topological vector space is a Baire space
Tadeusz Dobrowolski, Mikołaj Krupski, Witold Marciszewski
We prove that every homogeneous countable dense homogeneous topological space containing a copy of the Cantor set is a Baire space. In particular, every countable dense homogeneous…
On uniformly continuous maps between function spaces
Rafal Gorak, Mikolaj Krupski, Witold Marciszewski
In this paper we develop a technique of constructing uni- formly continuous maps between function spaces Cp(X) endowed with the pointwise topology. We prove that if a space X is co…
On functional tightness of infinite products
Mikołaj Krupski
A classical theorem of Malykhin says that if is a family of compact spaces such that , for every , then $t\left( \prod_{α\leq κ} X_α\right)\l…
On the weak and pointwise topologies in function spaces II
Mikołaj Krupski, Witold Marciszewski
For a compact space we denote by () the space of continuous real-valued functions on endowed with the weak (pointwise) topology. In this paper we discuss t…
On the weak and pointwise topologies in function spaces
Mikołaj Krupski
For a compact space we denote by () the space of continuous real-valued functions on endowed with the weak (pointwise) topology. In this paper we address t…
A metrizable with not homeomorphic to
Mikołaj Krupski, Witold Marciszewski
We give an example of an infinite metrizable space such that the space , of continuous real-valued function on endowed with the pointwise topology, is not homeomorp…
Topological dimension of a space is determined by the pointwise topology of its function space
Mikołaj Krupski
This paper has been withdrawn by the author
A note on condensations of function spaces onto -compact and analytic spaces
Mikołaj Krupski
Modifying a construction of W. Marciszewski we prove (in ZFC) that there exists a subspace of the real line , such that the realcompact space of continuous rea…
Some remarks on universality properties of
Mikolaj Krupski, Witold Marciszewski
We prove that if continuum is not a Kunen cardinal, then there is a uniform Eberlein compact space such that the Banach space does not embed isometrically into $\ell_\in…
On the t-equivalence relation
Mikolaj Krupski
For a completely regular space , denote by the space of continuous real-valued functions on , with the pointwise convergence topology. In this article we strengthen…
A dichotomy for the convex spaces of probability measures
Mikołaj Krupski, Grzegorz Plebanek
We show that every nonempty compact and convex space M of probability Radon measures either contains a measure which has `small' local character in M or else M contains a measure o…