Topology question

Forum for the GRE subject test in mathematics.
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ajf
Posts: 6
Joined: Mon Aug 31, 2009 1:43 am

Topology question

Post by ajf » 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.

thejudge
Posts: 1
Joined: Fri Sep 11, 2009 9:32 am

Re: Topology question

Post by thejudge » Fri Sep 11, 2009 9:36 am

Consider the union of the open sets about each x in A, then apply the second part of the definition of a topological space..

ajf
Posts: 6
Joined: Mon Aug 31, 2009 1:43 am

Re: Topology question

Post by ajf » Tue Sep 15, 2009 9:05 pm

I thought that that was the approach to take but I was not certain of how to formulate the solution. Thank you again for the help.



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