الفهرس 
Topological Vector SpacesOnly 14 pages are availabe for public view
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Abstract
Summary
It is well known that a normed space E is uniformly convex (smooth)
normed space if and only if its dual E∗ is uniformly smooth (convex).
We extend these geometric properties to seminormed spaces and then
introduce definitions of uniformly convex (smooth) countably seminormed
spaces. A new vision of the completion of countably seminormed
space was helpful in our task. We get some fundamental links
between Lindenstrauss duality formulas. A duality property between
uniform convexity and uniform smoothness of countably seminormed
space is also given.
Also we give a definition of countably normed space associated with
countably seminormed space with compatible seminorms and a definition
of Metric projection in a countably seminormed space.
This M. Sc. thesis is organized as follows:
1. Introduction, we show the importance of locally convex spaces
and we give a general view of what we have been done in this
thesis.
2. In chapter #1, we give a summary of topolpgical spaces [1], a
directed system [1], topological vector spaces [2], Hausdorff topological
vector Spaces [2] and quotient topological vector spaces [2]
almost of the details needed in this thesis.
3. In chapter #2, we study locally convex spaces [2], seminorms [2]
and metrizable topological vector spaces [2].
4. In chapter #3, we study completion of different spaces (Metric
space [5], normed space by using the technique of associated