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