Heinz-Peter Butzmann, Bernhard Buck
Free Commutative Convergence Groups
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 51, 159-166(1997)
MSC:
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
54A99 None of the above but in this section
Abstract: Apart from their theoretical interest, free topological objects are also a
resource for counterexamples. So the free commutative group over a
completely regular, non-normal topological space is an example of a
non-normal topological group. In this paper we construct the free
commutative convergence group ${\cal A}_c(X)$ over a Hausdorff convergence space $X$.
We show that it is a complete, Hausdorff convergence group and that $X$ can
be embedded as a closed subspace into ${\cal A}_c(X)$.
Notes: Abstract contains the first few lines of text of the paper.