User jkjium - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T10:33:46Z http://mathoverflow.net/feeds/user/6324 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/25977/how-to-understand-the-concept-of-compact-space How to understand the concept of compact space jkjium 2010-05-26T08:40:13Z 2010-05-26T15:08:46Z <p>the definition of compact space is: A subset K of a metric space X is said to be compact if every open cover of K contains finite subcovers. What is the meaning of defining a space is "compact". I found the explanation on wikipedia : "In mathematics, more specifically general topology and metric topology, a compact space is an abstract mathematical space in which, intuitively, whenever one takes an infinite number of "steps" in the space, eventually one must get arbitrarily close to some other point of the space. " I can not understand it, or at least I can not get this by its definition. Can anybody help me?</p> http://mathoverflow.net/questions/25977/how-to-understand-the-concept-of-compact-space/25981#25981 Comment by jkjium jkjium 2010-05-26T10:07:41Z 2010-05-26T10:07:41Z Your answer gives me a very intuitive view to compactness! Thanks very much! http://mathoverflow.net/questions/25977/how-to-understand-the-concept-of-compact-space Comment by jkjium jkjium 2010-05-26T09:13:01Z 2010-05-26T09:13:01Z Thanks very much! Your comments do make sense to me:)