Displaying similar documents to “Equation $f(p(x)) = q(f(x))$ for given real functions $p$, $q$”

A note on normal varieties of monounary algebras

Ivan Chajda, Helmut Länger (2002)

Czechoslovak Mathematical Journal

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A variety is called normal if no laws of the form s = t are valid in it where s is a variable and t is not a variable. Let L denote the lattice of all varieties of monounary algebras ( A , f ) and let V be a non-trivial non-normal element of L . Then V is of the form M o d ( f n ( x ) = x ) with some n > 0 . It is shown that the smallest normal variety containing V is contained in H S C ( M o d ( f m n ( x ) = x ) ) for every m > 1 where C denotes the operator of forming choice algebras. Moreover, it is proved that the sublattice of L consisting of all normal...

Some monounary algebras with EKP

Emília Halušková (2020)

Mathematica Bohemica

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An algebra 𝒜 is said to have the endomorphism kernel property (EKP) if every congruence on 𝒜 is the kernel of some endomorphism of 𝒜 . Three classes of monounary algebras are dealt with. For these classes, all monounary algebras with EKP are described.

Some remarks on Q -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

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We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that ℓ p , ( 1 ≤ p ≤ ∞ ) are Q algebras and that A n = ℨ L 1 ( Z ; 1 + | n | α ) is a Q -algebra if and only if α > 1 / 2 .

A note on splittable spaces

Vladimir Vladimirovich Tkachuk (1992)

Commentationes Mathematicae Universitatis Carolinae

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A space X is splittable over a space Y (or splits over Y ) if for every A ⊂ X there exists a continuous map f : X → Y with f - 1 f A = A . We prove that any n -dimensional polyhedron splits over 𝐑 2 n but not necessarily over 𝐑 2 n - 2 . It is established that if a metrizable compact X splits over 𝐑 n , then dim X ≤ n . An example of n -dimensional compact space which does not split over 𝐑 2 n is given.