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1
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Universally Kuratowski–Ulam Spaces And Open-Open Games

100%
Kalemba P., Kucharski A.
Annales Mathematicae Silesianae
|
2015
|
tom 29
|
nr 1
85-92
EN
We examine the class of spaces in which the second player has a winning strategy in the open-open game. We show that this spaces are not universally Kuratowski–Ulam. We also show that the games G and G7 introduced by P. Daniels, K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205–220] are not equivalent.
2
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A spectral characterization of skeletal maps

81%
Banakh T., Kucharski A., Martynenko M.
Open Mathematics
|
2013
|
tom 11
|
nr 1
161-169
EN
We prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between ω-spectra with surjective limit projections.
3
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Skeletally Dugundji spaces

81%
Kucharski A., Plewik S., Valov V.
Open Mathematics
|
2013
|
tom 11
|
nr 11
1949-1959
EN
We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. Our main result states that the following conditions are equivalent for a given space X: (i) X is skeletally Dugundji; (ii) every compactification of X is co-absolute to a Dugundji space; (iii) every C*-embedding of the absolute p(X) in another space is strongly π-regular; (iv) X has a multiplicative lattice in the sense of Shchepin [Shchepin E.V., Topology of limit spaces with uncountable inverse spectra, Uspekhi Mat. Nauk, 1976, 31(5), 191–226 (in Russian)] consisting of skeletal maps.
4
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Boolean algebras admitting a countable minimally acting group

81%
Błaszczyk A., Kucharski A., Turek S.
Open Mathematics
|
2014
|
tom 12
|
nr 1
46-56
EN
The aim of this paper is to show that every infinite Boolean algebra which admits a countable minimally acting group contains a dense projective subalgebra.
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