Complete proofs are given, requiring only elementary homotopy theory as background, of certain theorems characterizing those spaces having the shape of simplicial complexes, and those pro-complexes having the pro-homotopy type of complexes.
Complete proofs are given, requiring only elementary homotopy theory as background, of certain theorems characterizing those spaces having the shape of simplicial complexes, and those pro-complexes having the pro-homotopy type of complexes.
The class of connectivity functions and two similarly defined classes are shown to be distinct.
For every zero-dimensional space E of non-measurable cardinality we construct a zero-dimensional, hereditarily realcompact, locally compact and locally countable space which cannot be embedded as a closed subspace into any topological power of the space E. Under the assumption that all cardinals are non-measurable it gives the result stated in the title.
This is an answer for a question raised by H. Herrlich
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