Abstract:Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the \v Cech-Lebesgue dimension and the height dimension of posets, respectively.
Keywords: \v Cech-Lebesgue dimension, height dimension of posets, dyadic expansion, rigged finite open covers, partition dimension
AMS Subject Classification: 54F45, 06A10