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Counting overweight spaces
Gerald Kuba
Let c=2^aleph0 denote the cardinality of the continuum and let a,b,k be infinite cardinal numbers with a<b\leq 2^a. We show that there exist precisely 2^b T0-spaces of size a and w…
Scattered and paracompact order topologies
Gerald Kuba
We show that (in ZFC) every infinite set S can be equipped with 2^|S| complete metrics which generate mutually non-homeomorphic scattered order topologies on S. Furthermore, we sho…
On the variety of Euclidean point sets
Gerald Kuba
We construct a continuum of non-homeomorphic compact subspaces of the real line R without singleton components. Thus from the purely topological point of view the real line contain…
On decompositions of the real line
Gerald Kuba
Let X_t be a totally disconnected subset of the real line R for each t in R. We construct a partition {Y_t | t in R} of R into nowhere dense Lebesgue null sets Y_t such that for ev…