en.wikipedia.org/wiki/Totally_disconnected_space

In topology and related branches of mathematics, a totally disconnected space is
a topological space that is maximally disconnected, in the sense that it has no ...

mathworld.wolfram.com/TotallyDisconnectedSpace.html

A totally disconnected space is a space in which all subsets with more than one
element are disconnected. In particular, if it has more than one element, it is a ...

pirate.shu.edu/~wachsmut/ira/topo/connect.html

An open set S is called disconnected if there are two open, non-empty sets U and
V ... A set S is called totally disconnected if for each distinct x, y S there exist ...

proofwiki.org/wiki/Definition:Totally_Disconnected

Sep 12, 2016 ... That is, a topological space is totally disconnected if it contains no non-
degenerate connected subsets, i.e. connected subsets containing more ...

math.stackexchange.com/questions/550650/product-of-totally-disconnected-space-is-totally-disconnected

Nov 3, 2013 ... I read that the cartesian product with the product topology of a family of totally
disconnected topological spaces is totally disconnected, too.

math.stackexchange.com/questions/141768/totally-disconnected-space

May 6, 2012 ... I strongly believe that a totally disconnected Hausdorff space has to have a
topology that contains all the singletons. However, I am not sure ...

www.emathzone.com/tutorials/general-topology/totally-disconnected-space.html

A topological space X is said to be totally disconnected space if any pair of
distinct of X can be separated by a disconnection of X . In other words, a
topological ...

topospaces.subwiki.org/wiki/Totally_disconnected_space

Jan 13, 2012 ... Examples. The rational numbers form a totally disconnected space. In fact, any
irrational number gives a disconnection by partitioning the ...

mathoverflow.net/questions/37392/totally-disconnected-and-zero-dimensional-spaces

Sep 1, 2010 ... When do the notions of totally disconnected space and zero-dimensional space
coincide? From what I gather, there are at least three common ...

www.encyclopediaofmath.org/index.php/Totally-disconnected_space

Jan 3, 2016 ... The topological product and the topological sum of totally-disconnected spaces,
as well as any subspace of a totally-disconnected space, are ...