  The Kaluza-Klein monopole has been recognized as a string background with
significant non-geometric features: it must appear "localized" to winding
strings to match the NS5-brane's localization on the T-dual circle. In this
work, we explicitly construct this T-dual system in the doubled geometry
formalism, which proves to successfully describe the duality despite a broken
isometry on one side of the duality pair. We further suggest an extension of
the doubled formalism to the gauged linear sigma models describing this system
(both bosonic and supersymmetric) and show that previous calculations of
worldsheet instanton effects are best understood in this doubled form.
