1 citations · 1 across the 6 of their papers we have counts for
7 papers
Transfinite dimensions
Gerald Kuba
Let H be a Hilbert space and let F be the family of all countable subsets of an orthonormal basis of H. We show that if F is infinite then F is equipollent with every linear basis…
On the distribution of reducible polynomials
Gerald Kuba
Let Y_n(t) denote the set of all polynomials over the ring Z which are reducible over the field Q and of degree n>1 and of height not greater than t. We show that the true order of…
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…
Increasing singular functions with arbitrary positive derivatives at densely lying points
Gerald Kuba
Let A be an arbitrary countable set of reals, for example A=Q. Let g be an arbitrary mapping from A into the positive reals, for example g(a)=2^a. We show how a strictly increasing…