Sets and graphs
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There are a couple of concepts I need clarification for:
1) If a set has no interior points, then is it necessarily closed? Isn't the empty set considered open?
2) If the graph of f: R -> R is connected, does it have to be continuous? In just Real -> Real aren't these definitions equivalent?
Thanks.
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Solution Summary
This helps clarify open and closed sets, and connected and continuous graphs.
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1) If a set has no interior points, it is not necessarily closed.
For example, X={1/n} is a set with no interior points, ...
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