Abstract
In every infinite-dimensional vector space we build a complete, non-locally convex linear Hausdorff topology under the prescribed condition that it shall be compatible with a bounded algebraic structure for the space, that is, it admits a bounded Hamel basis whose coefficient linear functionals are continuous. As a byproduct, we obtain the existence of non-locally convex topologies having the approximate and fixed point property as prescribed conditions. The obstruction of bounded Hamel bases by complete vector topologies on linear space of countable dimension is also discussed.
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