I l Show that if X has the discrete topology, then its only connected subspaces are point sets. Solution Let X have discrete topology. Any subset Y of X is the union of singletons , each of which is both open and closed (as X has discrete topology) So the maximal sets which cannot expressed as a disjoint union of open (closed) subsets are the singletons. Hence the connected components of X are the singletons..

1. I l
Show that if X has the discrete topology, then its only connected subspaces are point sets.
Solution
Let X have discrete topology.
Any subset Y of X is the union of singletons , each of which is both open and closed (as X has
discrete topology)
So the maximal sets which cannot expressed as a disjoint union of open (closed) subsets are the
singletons.
Hence the connected components of X are the singletons.