Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 12 1 2021 05 01 Continuity in fundamental locally multiplicative topological algebras 129 141 4685 10.22075/ijnaa.2019.13751.1715 EN Ali Naziri-Kordkandi Department of Mathematics, Payame Noor University,Iran Ali Zohri Department of Mathematics, Payame Noor University,Iran Fariba Ershad Department of Mathematics, Payame Noor University,Iran Bahman Yousefi Department of Mathematics, Payame Noor University,Iran Journal Article 2018 01 19 Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras. https://ijnaa.semnan.ac.ir/article_4685_ff241d794c4e5912b4864a77af09ab85.pdf