I l Show that if X has the discrete topology, then its only conn.pdf
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In a space with discrete topology, the only connected subspaces are single-point sets. Any subset can be expressed as a union of singletons, which are both open and closed. Therefore, the only connected components in such a space are the individual singletons.
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I l Show that if X has the discrete topology, then its only conn.pdf
- 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.