Filling the gaps in an unpublished example of Nyikos: a countably compact non-compact manifold under $\clubsuit_C$

We provide details for a Theorem which is only available on a unfinished preliminary draft of P.

Nyikos: the existence under $\clubsuit_C$ of a hereditarily collectionwise normal countably compact non-compact manifold which does not contain a copy of $\omega_1$.

This shows in particular that {\bf MA + $\neg$CH} does not imply the existence of a copy of $\omega_1$ in a countably compact non-compact manifold (it is known that {\bf PFA} does imply it).

The said manifold is obtained from a principal $\mathbb{S}^1$-bundle over the long ray, and some structural Theorems for these spaces (due to Nyikos as well) are also proved.

We show that the same type of theorems hold for $n$-to-$1$ closed preimages of $\omega_1$ and $\mathbb{Z}_n$-``bundles'' over $\omega_1$, where $\mathbb{Z}_n$ is the additive group of integers modulo $n$.

A small generalization of $\clubsuit_C$ is also quickly investigated.