Document Type : Research Paper


Department of Mathematics, Sahand university of technology, Tabriz- Iran


In this paper, the gradual real numbers are considered and the
notion of the gradual normed linear space is given. Also some topological
properties of such spaces are studied, and it is shown that the gradual normed
linear space is a locally convex space, in classical sense. So the results in locally
convex spaces can be translated in gradual normed linear spaces. Finally, we
give an example of a gradual normed linear space which is not normable in
classical analysis.


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