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
The main purpose of this paper is to unify a number of theorems in topology whose conclusions state that a product of topological spaces has a compactness-like property.Three such theorems are (1) the Tychonoff theorem: Every product of compact spaces is compact, (2) the theorem of C.T. Scarborough and A.H. Stone: Every product of at most N1 sequentially compact spaces is countably compact, and (3) the theorem of N. Noble: A countable product of Lindelöf P-spaces is Lindelöf.
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