  In this paper, we clarify the relationship among the Vietoris-type homology
theories and the microsimplicial homology theories, where the latter are
nonstandard homology theories defined by M. C. McCord (for topological spaces),
T. Korppi (for completely regular topological spaces) and the author (for
uniform spaces). We show that McCord's and our homology are isomorphic for all
compact uniform spaces and that Korppi's and our homology are isomorphic for
all fine uniform spaces. Our homology shares many good properties with Korppi's
homology. As an example, we outline a proof of the continuity of our homology
with respect to uniform resolutions. S. Garavaglia proved that McCord's
homology is isomorphic to Vietoris homology for all compact topological spaces.
Inspired by this result, we prove that our homology is isomorphic to uniform
Vietoris homology for all precompact uniform spaces and that Korppi's homology
is isomorphic to normal Vietoris homology for all pseudocompact completely
regular topological spaces.
