Browsing by Author "Ercan, Zafer"
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All Topologies Come from a Family of 01Valued Quasimetrics
Ercan, Zafer; Vural, Mehmet (Springer Singapore Pte Ltd, 2019)We prove the statement in the title. This reproves that every topological space is induced by a quasiuniformity. 
An answer to a question on the affine bijections on C(X, I)
Ercan, Zafer; Önal, Süleyman (Natl Inquiry Services Centre Pty Ltd, 2009)A complete description of the bijective a. ne map on C(X, I) is given. This provides an answer to a question of [2] on the affine bijections on C(X, I). 
The BanachStone theorem revisited
Ercan, Zafer; Önal, S. (Elsevier B.V. All, 2008)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 1biseparating Riesz isomorphism then X and Y are homeomorphic, and E and F are Riesz isomorphic. This ... 
A characterization of riesz nmorphisms and applications
Ercan, Zafer; Önal, Süleyman (Taylor & Francis Inc, 2008)Let X1 I X2,..., Xn be realcompact spaces and Z he a topological space. Let pi : C(X1)X C(X2) X... X C(Xn)> C(Z) be a Riesz nmorphism. We show that there exist functions sigma(i) : Z > Xi (i = 1, 2,..., n) and w ... 
A characterization of uuniformly completeness of Riesz spaces in terms of statistical Uuniformly precompleteness
Ercan, Zafer (Walter de Gruyter GmbH, 2009)In this paper we introduce statistically uuniformly convergent sequences in Riesz spaces (vector lattices) and then we give a characterization of uuniformly completeness of Riesz spaces. © 2009 Warsaw University. All ... 
Characterizations of riesz spaces with bproperty
Alpay, Şafak; Ercan, Zafer (Springer, 2009)A Riesz space E is said to have bproperty if each subset which is order bounded in Esimilar to similar to is order bounded in E. The relationship between bproperty and completeness, being a retract and the absolute weak ... 
Every norm is a restriction of an orderunit norm
Çağlar, Mert; Ercan, Zafer (2016)We point out the equivalence of the fact that every norm on a vector space is a restriction of an orderunit norm to that of Paulsen’s construction concerning generalization of operator systems. 
Invariant subspaces for positive operators on locally convex solid Riesz spaces
Çağlar, Mert; Ercan, Zafer (Elsevier Science Bv, 2007)We prove that an x(0)quasinilpotent semigroup S of continuous positive linear operators on a locally convex solid Riesz space X has a common invariant subspace. Using this, a result which implies the main theorem of ... 
MazurUlam theorem for riesz spaces
Çelik, Cesim; Ercan, Zafer (Walter De Gruyter Gmbh, 2010)We give a MazurUlam type theorem for Riesz spaces. In particular, a generalization of the MazurUlam theorem is given in terms of a lattice normed space. 
Memorandum on multiplicative bijections and order
Cabello Sanchez, Felix; Cabello Sanchez, Javier; Ercan, Zafer; Önal, Süleyman (Springer, 2009)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 ... 
A note on the main inclusion theorem of Luxemburg and Zaanen
Ercan, Zafer (2013)We give a more elementary proof of the main statement of the proof of the main result in [8]. Following the idea of [8], we reprove a result of Luxemburg and Zaanen, that is, an Archimedean Riesz space is Dedekind complete ... 
On KakutaniKrein and MaedaOgasawara spaces
Ercan, Zafer; Tan, Neşet Özkan (Scientific Technical Research Council TurkeyTubitak, 2014)Let E be an Archimedean Riesz space. It is shown that the KakutaniKrein space of the center of the Dedekind completion of E and the MaedaOgasawara space of E are homeomorphic. By applying this, we can reprove a Banach ... 
On the end of the cone metric space
Ercan, Zafer (Elsevier Science Bv, 2014)Starting with the initial paper of Huang and Zhang [2] in 2007, more than six hundred papers dealing with cone metric spaces have been published so far. In this short note we present a different proof of the known fact ... 
Orderunitmetric Spaces
Çağlar, Mert; Ercan, Zafer (Springer, 2014)We study the concept of cone metric space in the context of ordered vector spaces by setting up a general and natural framework for it. 
A remark on the paper "Laterally closed lattice homomorphisms"
Ercan, Zafer (Springer, 2014)A new and simple proof of the main result of the paper "Laterally closed lattice homomorphisms" by Toumi and Toumi (J Math Anal Appl 324:11781194, 2006) is given following the paper "Extension of Riesz homomorphisms, I" ... 
Riesz spaces of measures on semirings
Ercan, Zafer (2009)It is shown that the spaces of finite valued signed measures (signed charges) on ?semirings (semirings) are Dedekind complete Riesz spaces, which generalizes known results on ?algebra and algebra cases.