1 citations · 1 across the 14 of their papers we have counts for
15 papers
Proper classes of non-embeddable continua
Gerald Kuba
Our main result is a construction of a class H of pathwise connected, locally connected, compact Hausdorff spaces such that (i) if X,Y are distinct spaces in H then a continuous, i…
Many coarse topologies on the real line
Gerald Kuba
Let c denote the cardinality of the continuum. Let L denote the family of all Hausdorff topologies on the real line coarser than the natural topology. We construct 2^c pairwise non…
Counting continua
Gerald Kuba
For infinite cardinals let denote the class of all compact Hausdorff spaces of weight and size . So if or . If F is a class of…
On real functions with graphs either connected or locally connected
Gerald Kuba
Let S denote the family of all subspaces of the plane that are graphs of functions from the real line R to itself. We prove that S has two subfamilies G,H of spaces such that the c…
Connected Hamel bases in Hilbert spaces
Gerald Kuba
Our main goal is to track down an algebraic basis of Hilbert space which is a connected and locally connected subset of the unit sphere.
On compact subsets of the plane
Gerald Kuba
We construct a family F of compact and pathwise connected subsets of the Euclidean plane such that (i) the cardinality of F is that of the continuum (and hence extremely large) and…
Many non-embeddable infinite groups
Gerald Kuba
Let K be a set of infinite cardinals such that the cardinality of K is the first strong limit cardinal greater than uncountably many strong limit cardinals. We construct a family o…
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…
Cantor sets and fields of reals
Gerald Kuba
Our main result is a construction of four families C_1,C_2,B_1,B_2 which are equipollent with the power set of the real line R and satisfy the following properties. (i) The members…
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…
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…