Understanding the Closed Mobius Strip: Get Help Here!

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Why Mobius strip closed?Mobius strip is compact because it is confined and closed. But I can't understand closed of Mobius strip. Help please.
 
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What is the meaning of closed (topology?) here? If you are talking about the ordinary topology, then, as long as the edges are included, every Cauchy sequence on the surface will have a limit on the surface.
 

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