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Directional derivatives in non-Hausdorff TVS: topological filter techniques without metric structures

In this work, we introduce and give some results about directional derivatives in non-Hausdorﬀ Topological Vector Space over general Topological Division Ring. Through the paper, we use some topological ﬁlter techniques that are needful for the development of the theory because of the total lack of a metric structure of the spaces, but most of all for the non-uniqueness of the limits due to the absence of the T2 bond.