  The group of compactly supported homeomorphisms on a Tychonoff space can be
topologized in a number of ways, including as a colimit of homeomorphism groups
with a given compact support, or as a subgroup of the homeomorphism group of
its Stone-\v{C}ech compactification. A space is said to have the Compactly
Supported Homeomorphism Property (CSHP) if these two topologies coincide. The
authors provide necessary and sufficient conditions for finite products of
ordinals equipped with the order topology to have CSHP. In addition, necessary
conditions are presented for finite products and coproducts of spaces to have
CSHP.
