The Banach-Stone theorem revisited

Date

2008-10-01

Author

ERCAN, ZAFER
Önal, Süleyman

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

134
views

0
downloads

Let X and Y be compact Hausclorff spaces, and E and F be locally solid Riesz spaces. If pi : C(X. E) -> C(Y, F) is a 1-biseparating Riesz isomorphism then X and Y are homeomorphic, and E and F are Riesz isomorphic. This generalizes the main results of [Z. Ercan, S. Onal, Banach-Stone theorem for Banach lattice valued continuous functions, Proc. Amer. Math. Soc. 135 (9) (2007) 2827-2829] and [X. Miao, C. Xinhe, H. Jiling, Banach-Stone theorems and Riesz algebras, J. Math. Anal. Appl. 313 (1) (2006) 177-183], and answers a conjecture in [Z. Ercan, S. Onal, Banach-Stone theorem for Banach lattice valued continuous functions. Proc. Amer. Math. Soc. 135 (9) (2007) 2827-2829].

Subject Keywords

Geometry and Topology

URI

https://hdl.handle.net/11511/46879

Journal

TOPOLOGY AND ITS APPLICATIONS

DOI

https://doi.org/10.1016/j.topol.2008.05.018

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Some cardinal invariants on the space C-alpha (X, Y) Onal, S; Vural, C (Elsevier BV, 2005-05-14) Let C-alpha (X, Y) be the set of all continuous functions from X to Y endowed with the set-open topology where a is a hereditarily closed, compact network on X such that closed under finite unions. We define two properties (E1) and (E2) on the triple (alpha, X, Y) which yield new equalities and inequalities between some cardinal invariants on C-alpha (X, Y) and some cardinal invariants on the spaces X, Y such as:
Some upper bounds for density of function spaces Önal, Süleyman (Elsevier BV, 2009-05-01) Let C-alpha(X, Y) be the set of all continuous functions from X to Y endowed with the set-open topology where alpha is a hereditarily closed, compact network on X which is closed Under finite unions. We proved that the density of the space C-alpha(X, Y) is at most iw(X) . d(Y) where iw(X) denotes the i-weight of the Tychonoff space X, and d(Y) denotes the density of the space Y when Y is an equiconnected space with equiconnecting function psi, and Y has a base consists of psi-convex Subsets of Y. We also pr...
An obstruction to the existence of real projective structures Coban, Hatice (Elsevier BV, 2019-09-15) In this short note, we give an obstruction to obtain examples of higher dimensional manifolds with infinite fundamental groups, including the infinite cyclic group Z, admitting no real projective structure.
On endomorphisms of surface mapping class groups Korkmaz, Mustafa (Elsevier BV, 2001-05-01) In this paper, we prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
Finite rigid sets in curve complexes of nonorientable surfaces Ilbira, Sabahattin; Korkmaz, Mustafa (Springer Science and Business Media LLC, 2020-06-01) A rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map from the set into the curve complex is induced by a homeomorphism of the surface. In this paper, we find finite rigid sets in the curve complexes of connected nonorientable surfaces of genus g with n holes for g + n not equal 4.

Citation Formats

Z. ERCAN and S. Önal, “The Banach-Stone theorem revisited,” TOPOLOGY AND ITS APPLICATIONS, pp. 1800–1803, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46879.