An Open Mapping Theorem
It is proved that any surjective morphism $f: \mathbb{Z}^κ\to K$ onto a locally compact group $K$ is open for every cardinal $κ$. This answers a question posed by Karl Heinrich Hofmann and the second author.
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arXiv subjects
S. A. Morris
Publications and source records attributed to S. A. Morris.
The free abelian topological group and the free locally convex space on the unit interval
We give a complete description of the topological spaces $X$ such that the free abelian topological group $A(X)$ embeds into the free abelian topological group $A(I)$ of the closed unit interval. In particular, the free abelian topological group $A(X)$ of any finite-dimensional compact metrizable space $X$ embeds into $A(I)$. The situation turns out to be somewhat different for free locally convex spaces. Some results for the spaces of continuous functions with the pointwise topology are also obtained. Proofs are based on the classical Kolmogorov's Superposition Theorem.
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