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ln this paper we study several topologies on unbounded operator algebras. The first purpose is to discuss the relations between the topologies on general unbounded operator algebras. Secondly we study the topologies on special unbounded operator algebras in details. Finally we study the relations between locally convex *-algebras and unbounded operator algebras.doi:10.2206/kyushumfs.33.355 fatcat:gi6chk36cnfldnv5azouuiqvdi