On the homology of compact spaces by using non-standard methods

It is proved that strong and Čech homology theories coincide for compact pairs and coefficients in an equationally compact group or in the non-standard group G ∗ for any abelian group G. It is also proved that McCord homology has compact supports to a reasonable degree. Furthermore, the equality of the homology classes of point embeddings into the 2-adic solenoid is studied using non-standard methods.