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Do you use open cover to define compactness?

@mathteacher : Sorry I am not actually conversant with that

By the way the statement is not true, we need M to be closed.

How you define compactness in your class? is it every open cover has finite subcover?

he used sequences, but I have seen you definition too

Ok, so you use every bounded sequence is convergent ?

yes

I just checked the course material he has the first definition also in it, so I think it can be used

You mean the open cover definition?

yes

good

Can you help if the definition is "X is compact if every sequence of X has a convergent subsequence