### Topology question

Posted:

**Fri Sep 11, 2009 4:33 am**I'm reviewing topology from Munkres' 1st book and need some help on exercise (1) on page 83. The question is

Let X be a topological space; let A be a subset of X. Suppose that for each x in A there is an open set U containing x such that U is a subset of A. Show that A is open in X.

Thanks in advance for the help. Also, I'm purchasing his latest book where I can find answers to the exercises on the Internet.

Let X be a topological space; let A be a subset of X. Suppose that for each x in A there is an open set U containing x such that U is a subset of A. Show that A is open in X.

Thanks in advance for the help. Also, I'm purchasing his latest book where I can find answers to the exercises on the Internet.