Let K be a first-order structure with a dimension function, satisfying some natural conditions. Let A be a definable set. If every point in A has a definable neighborhood in A with dimension less than p, then A has dimension less than p.
Dimension in topological structures: Topological closure and local property / Fornasiero, Antongiulio; Halupczok, Immanuel. - STAMPA. - 576:(2012), pp. 89-94. (Intervento presentato al convegno Groups and Model Theory) [10.1090/conm/576/11335].
Dimension in topological structures: Topological closure and local property
Fornasiero, Antongiulio;
2012
Abstract
Let K be a first-order structure with a dimension function, satisfying some natural conditions. Let A be a definable set. If every point in A has a definable neighborhood in A with dimension less than p, then A has dimension less than p.
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