Van der Walt, Jan Harm2016-03-012016Jan Harm van der Walt (2016) A closed graph theorem for order bounded operators, Quaestiones Mathematicae, 39:2, 167-178, DOI: 10.2989/16073606.2015.1068235.0379-9468 (print)1727-933X (online)10.2989/16073606.2015.1068235http://hdl.handle.net/2263/51637The closed graph theorem is one of the cornerstones of linear functional analysis in Frechet spaces, and the extension of this result to more general topological vector spaces is a difficult problem comprising a great deal of technical difficulty. However, the theory of convergence vector spaces provides a natural framework for closed graph theorems. In this paper we use techniques from convergence vector space theory to prove a version of the closed graph theorem for order bounded operators on Archimedean vector lattices. This illustrates the usefulness of convergence spaces in dealing with problems in vector lattice theory, problems that may fail to be amenable to the usual Hausdorff-Kuratowski-Bourbaki concept of topology.en© Taylor and Francis. This is an electronic version of an article published in Quaestiones Mathematicae, vol. 39, no. 2, pp. 167-178, 2016. doi : 10.2989/16073606.2015.1068235. Quaestiones Mathematicae is available online at : http://www.tandfonline.comloi/tqma20.Vector latticeConvergence vector spaceOrder bounded operatorPostprint Article