Memorandum on multiplicative bijections and order

Cabello Sanchez, Felix
Cabello Sanchez, Javier
Önal, Süleyman
Let C(X, I) denote the semigroup of continuous functions from the topological space X to I = [0, 1], equipped with the pointwise multiplication. The paper studies semigroup homomorphisms C(Y, I) -> C(X, I), with emphasis on isomorphisms. The crucial observation is that, in this setting, homomorphisms preserve order, so isomorphisms preserve order in both directions and they are automatically lattice isomorphisms. Applications to uniformly continuous and Lipschitz functions on metric spaces are given. Sample result: if Y and X are complete metric spaces of finite diameter without isolated points, every multiplicative bijection T : Lip(Y, I) -> Lip(X, I) has the form Tf = f circle tau, where tau : X -> Y is a Lipschitz homeomorphism.


Some maximal function fields and additive polynomials
GARCİA, Arnaldo; Özbudak, Ferruh (Informa UK Limited, 2007-01-01)
We derive explicit equations for the maximal function fields F over F-q(2n) given by F = F-q(2n) (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field F-q(2n), and where A(Y) is q- additive and deg(f) = q(n) + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over F-q(2n) (i.e., the extension H/F is Galois).
Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Value sets of Lattes maps over finite fields
Küçüksakallı, Ömer (Elsevier BV, 2014-10-01)
We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
On the deformation chirality of real cubic fourfolds
Finashin, Sergey (Wiley, 2009-09-01)
According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
On algebraic K-theory of real algebraic varieties with circle action
Ozan, Yıldıray (Elsevier BV, 2002-05-24)
Assume that X is a compact connected orientable nonsingular real algebraic variety with an algebraic free S-1-action so that the quotient Y=X/S-1 is also a real algebraic variety. If pi:X --> Y is the quotient map then the induced map between reduced algebraic K-groups, tensored with Q, pi* : (K) over bar (0)(R(Y, C)) circle times Q --> (K) over bar (0)(R(X, C)) circle times Q is onto, where R(X, C) = R(X) circle times C, R(X) denoting the ring of entire rational (regular) functions on the real algebraic va...
Citation Formats
F. Cabello Sanchez, J. Cabello Sanchez, Z. ERCAN, and S. Önal, “Memorandum on multiplicative bijections and order,” SEMIGROUP FORUM, pp. 193–209, 2009, Accessed: 00, 2020. [Online]. Available: