Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
uτ-Convergence in locally solid vector lattices
Download
index.pdf
Date
2018
Author
Dabboorasad, Yousef A M
Metadata
Show full item record
Item Usage Stats
173
views
47
downloads
Cite This
We say that a net (xα) in a locally solid vector lattice (X,τ) is uτ-convergent to a vector x ∈ X if
Subject Keywords
Lattice theory.
,
Vector spaces.
,
Convergence.
URI
http://etd.lib.metu.edu.tr/upload/12622008/index.pdf
https://hdl.handle.net/11511/27225
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
um-Topology in multi-normed vector lattices
Dabboorasad, Y. A.; Emelyanov, Eduard; Marabeh, M. A. A. (2018-04-01)
Let be a separating family of lattice seminorms on a vector lattice X, then is called a multi-normed vector lattice (or MNVL). We write if for all . A net in an MNVL is said to be unbounded m-convergent (or um-convergent) to x if for all . um-Convergence generalizes un-convergence (Deng et al. in Positivity 21:963-974, 2017; KandiAc et al. in J Math Anal Appl 451:259-279, 2017) and uaw-convergence (Zabeti in Positivity, 2017. doi:10.1007/s11117-017-0524-7), and specializes up-convergence (AydA +/- n et al. ...
Nonstandard hulls of lattice-normed ordered vector spaces
Aydin, Abdullah; Gorokhova, Svetlana; Gul, Hasan (2018-01-01)
Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.
Model-theory of vector-spaces over unspecified fields
Pierce, David (2009-06-01)
Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector...
o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces
Alpay, Safak; Emelyanov, Eduard; Gorokhova, Svetlana (2022-06-01)
We investigate o tau-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the Kantorovich-Banach operators between locally solid lattices and topological vector spaces; and the Levi operators from locally solid lattices to vector lattices. The main idea of operator versions of notions related to vector lattices lies in redistributing topological and order properties of a topological vector lattice between the domain and range of an operator under investigation...
SPACES OF u tau-DUNFORD-PETTIS AND u tau-COMPACT OPERATORS ON LOCALLY SOLID VECTOR LATTICES
ERKURŞUN ÖZCAN, NAZİFE; Gezer, Niyazi Anıl; Zabeti, Omid (2019-01-01)
Suppose X is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on X. In this paper, we consider some situations under which these classes of bounded operators form locally solid vector lattices. In addition, we generalize some notions of uaw-Dunford-Pettis operators and uaw-compact operators defined on a Banach lattice to general theme of locally solid vector lattices. With the aid of appropriate topologies, we investigate some relations between to...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
Y. A. M. Dabboorasad, “uτ-Convergence in locally solid vector lattices,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.