On characterization of a Riesz homomorphism on C(X)-space

Önal, Süleyman
Let X be a realcompact space. We present a very simple and elementary proof of the well known fact that every Riesz homomorphism pi : C(X) -> R is point evaluated. Moreover, the proof is given in ZF.


A remark on the homomorphism on C(X)
Ercan, Z; Onal, S (American Mathematical Society (AMS), 2005-01-01)
Let X be a real compact space. Without using the axiom of choice we present a simple and direct proof that a non-zero homomorphism on C(X) is determined by a point.
Piecewise polynomials with different smoothness degrees on polyhedral complexes
ALTINOK BHUPAL, SELMA; Sipahi, Neslihan Os (Informa UK Limited, 2019-05-01)
For a given d-dimensional polyhedral complex Delta and a given degree k, we consider the vector space of piecewise polynomial functions on Delta of degree at most k with a different smoothness condition on each pair of adjacent d-faces of Delta. This is a finite dimensional vector space. The fundamental problem in Approximation Theory is to compute the dimension of this vector space. It is known that the dimension is given by a polynomial for sufficiently large k via commutative algebra. By using the techni...
On homology of real algebraic varieties
Ozan, Yıldıray (American Mathematical Society (AMS), 2001-01-01)
Let R be a commutative ring with unity and X an R-oriented compact nonsingular real algebraic variety of dimension n. If i : X --> X-C is any nonsingular complexification of X, then the kernel, which we will denote by KHk(X, R), of the induced homomorphism i(*) : H-k(X, R) --> H-k(X-C, R) is independent of the complexification. In this work, we study KHk(X, R) and give some of its applications.
Invariant subspaces for Banach space operators with an annular spectral set
Yavuz, Onur (2008-01-01)
Consider an annulus Omega = {z epsilon C : r(0) 0 such that parallel to p(T)parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} and parallel to p(r(0)T(-1))parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} for all polynomials p. Then there exists a nontrivial common invariant subspace for T* and T*(-1).
An obstruction to finding algebraic models for smooth manifolds with prescribed algebraic submanifolds
CELIKTEN, A; Ozan, Yıldıray (2001-03-01)
Let N ⊆ M be a pair of closed smooth manifolds and L an algebraic model for the submanifold N. In this paper, we will give an obstruction to finding an algebraic model X of M so that the submanifold N corresponds in X to an algebraic subvariety isomorphic to L.
Citation Formats
Z. M. AKKAR ERCAN and S. Önal, “On characterization of a Riesz homomorphism on C(X)-space,” QUAESTIONES MATHEMATICAE, pp. 147–150, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43144.