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Keywords:
embedding; separating points from closed sets; weak separating points from closed sets; separating family; weight
embedding; separating points from closed sets; weak separating points from closed sets; separating family; weight
Summary:
Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski's topological calculus.
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