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Given a topological space that is T3 (i.e. regular) and has a sigma-discrete base (where these conditions allow the topological space to be biconditionally metrizable), is there a way to understand what all the possible admittable metrics are? And do all these possibly admittable metrics form a space?

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    I just wanted to know whether or not such spaces had been studied, and if there is a sophisticated way of analysing them.2011-02-17

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