One-sided -ideals and -ideals in semirings.
Weinert, H.J., Sen, M.K., Adhikari, M.R. (1996)
Mathematica Pannonica
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Weinert, H.J., Sen, M.K., Adhikari, M.R. (1996)
Mathematica Pannonica
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Bohumil Šmarda (1980)
Archivum Mathematicum
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Keiji Izuchi (1976)
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Kondo, Michiro (2001)
International Journal of Mathematics and Mathematical Sciences
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David Rudd (1975)
Fundamenta Mathematicae
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Aldo Ursini (1984)
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Imrich Fabrici (1981)
Mathematica Slovaca
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Jörg Brendle, Diego Alejandro Mejía (2014)
Fundamenta Mathematicae
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The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even...
Víctor M. Sánchez (2017)
Open Mathematics
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There are just a few general criteria on spaceability. This survey paper is the history of one of the first ones. Let I1 and I2 be arbitrary operator ideals and E and F be Banach spaces. The spaceability of the set of operators I1(E, F) I2(E, F) is studied. Before stating the criterium, the paper summarizes the main results about lineability and spaceability of differences between particular operator ideals obtained in recent years. They are the seed of the ideas contained in the general...