Rather, boundedness is an underlying semantic distinction that motivates countability. A second-countable space is said to satisfy the second axiom of countability. Note that boundedness in nouns should not be thought of as synonymous with countability. Second countability is automatic for compact Riemann surfaces. Cantor's article introduced the uncountability theorem and the concept of countability. For example, second countability and metrisability are hereditary properties. Other properties, such as countability, are not absolute.