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](https://proofwiki.org/wiki/Definition:Continuum_(Topology) "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](https://math.stackexchange.com/questions/2500367/non-metric-topological-continua) on math.stackexchange but did not get any answer.



Non-metric topological continua
A good starting point for studying countinua in the sense of the definition (2), i.e., compact Hausdorff spaces, is the survey paper "Continuum Theory (General)" by Ed Tymchatyn in [Encyclopedia of General Topology](http://www.sciencedirect.com/science/book/9780444503558).
This paper contains further references.


As an example of a non-trivial result holding for both definitions (1) and (2) one can mention that the superextension of a compact Hausdorff space is connected and locally connected. This can be found in the [old book](https://books.google.com.ua/books/about/Supercompactness_and_Wallman_Spaces.html?id=LqPQAAAAMAAJ&redir_esc=y) of van Mill.


