TITLE: Non-metric topological continua
QUESTION [6 upvotes]: What important results hold for non-metric continua, or where can I find a survey of such results?
There are three definitions of a continuum around: a non-empty topological space that is
(1) connected compact metric, or
(2) connected compact Hausdorff [e.g., General Topology by Willard], or
(3) connected compact [ProofWiki].
I am interested in non-trivial properties commonly known for definition (1) that have been found to also hold for definitions (2) or even (3).

REPLY [3 votes]: My old theorem (i.e. by Włodzimierz Holsztyński) about maps of inverse limits of ANRs, which involves universal mappings, holds for general Hausdorff compact spaces. Since image domains of universal maps are connected, this means that this theorem is about general Hausdorff compact continua. (I very soon had another and a much more elegant proof, and I had presented it many times publicly but not in print; I didn't use Smith-Moore general sequences in that newer proof).
There are many results in the theory of fixed points, in dimension theory and universal mappings which hold for general Hausdorff continua, it's only natural. Basically, most every topological theorem about metric metric continua allows for a Hausdorff compact version, and in practice the formulation of the generalization is natural.