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Displaying similar documents to “On almost normal subgroups of supersoluble groups”

Continuous functions between Isbell-Mrówka spaces

Salvador García-Ferreira (1998)

Commentationes Mathematicae Universitatis Carolinae

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Let Ψ ( Σ ) be the Isbell-Mr’owka space associated to the M A D -family Σ . We show that if G is a countable subgroup of the group 𝐒 ( ω ) of all permutations of ω , then there is a M A D -family Σ such that every f G can be extended to an autohomeomorphism of Ψ ( Σ ) . For a M A D -family Σ , we set I n v ( Σ ) = { f 𝐒 ( ω ) : f [ A ] Σ for all A Σ } . It is shown that for every f 𝐒 ( ω ) there is a M A D -family Σ such that f I n v ( Σ ) . As a consequence of this result we have that there is a M A D -family Σ such that n + A Σ whenever A Σ and n < ω , where n + A = { n + a : a A } for n < ω . We also notice that there is no M A D -family...

Condensations of Cartesian products

Oleg I. Pavlov (1999)

Commentationes Mathematicae Universitatis Carolinae

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We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space X there is a μ such that X μ can be condensed onto a normal ( σ -compact) space if and only if there is no measurable cardinal. For any Tychonoff space X and any cardinal ν there is a Tychonoff space M which preserves many properties of X and such that any one-to-one continuous image of M μ , μ ν , contains a...

Methods of analysis of the condition for correct solvability in L p ( ) of general Sturm-Liouville equations

Nina A. Chernyavskaya, Leonid A. Shuster (2014)

Czechoslovak Mathematical Journal

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We consider the equation - ( r ( x ) y ' ( x ) ) ' + q ( x ) y ( x ) = f ( x ) , x ( * ) where f L p ( ) , p ( 1 , ) and r > 0 , q 0 , 1 r L 1 loc ( ) , q L 1 loc ( ) , lim | d | x - d x d t r ( t ) · x - d x q ( t ) d t = . In an earlier paper, we obtained a criterion for correct solvability of ( * ) in L p ( ) , p ( 1 , ) . In this criterion, we use values of some auxiliary implicit functions in the coefficients r and q of equation ( * ). Unfortunately, it is usually impossible to compute values of these functions. In the present paper we obtain sharp by order, two-sided estimates (an estimate of a function f ( x ) for x ( a , b ) through a function g ( x ) is sharp by order if c - 1 | g ( x ) | | f ( x ) | c | g ( x ) | , ...