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).
I have asked this question on math.stackexchange but did not get any answer.