Mabula, Mokhwetha DanielCobzas, Stefan2017-02-142017-02-142015-04Mabula, MD & Cobzas, S 2015, 'Zabrejko's lemma and the fundamental principles of functional analysis in the asymmetric case', Topology and its Applications, vol. 184, pp. 1-15.0166-864110.1016/j.topol.2015.01.010http://hdl.handle.net/2263/59029Some versions of the fundamental principles of the functional analysis in asymmetric normed spaces – the Open Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Principle – are proved. The proofs are based on an asymmetric version of a lemma of Zabreijko on the continuity of the countably subadditive functionals. At the same time a flaw in the proof of the Uniform Boundedness Principle, given in the book by Cobzaş (2013), is fixed.en© 2015 Elsevier B.V. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Topology and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Topology and its Applications, vol. 184, pp. 1-15, 2015. doi : 10.1016/j.topol.2015.01.010.Asymmetric normed spaceUniform boundedness principleOpen mapping theoremClosed graph theoremBaire categoryBitopological spacePostprint Article