diff --git a/theorems/T000701.md b/theorems/T000701.md new file mode 100644 index 000000000..dce530322 --- /dev/null +++ b/theorems/T000701.md @@ -0,0 +1,23 @@ +--- +uid: T000701 +if: + and: + - P000126: true + - P000036: true + - P000203: false +then: + P000039: true +refs: +- zb: "1400.39025" + name: Connected door spaces and topological solutions of equations (Wu, Wang, Zhang) +--- + +According to Theorem 1 in {{zb:1400.39025}}, there are three types of connected door spaces: +- an *excluded point topology* (like {S12}), +which is almost discrete; +- a *particular point topology* (like {S8}), +which is hyperconnected; +- a *free ultrafilter topology* (like {S145}), +which is hyperconnected. + +So, if a connected door space is not almost discrete, it must be hyperconnected.