This property is not closed, but a function is continuous if and only if its inverse preserves this property.
This property is preserved by a map between Banach spaces if that map is bounded, surjective, and linear. The Baire Category Theorem characterizes spaces in which a countable intersection of dense sets with this property is also dense. In complex analysis, non-constant analytic functions on a region preserve this property. This property is not closed, but a function is continuous if and only if its inverse preserves this property. A topology is defined with a collection of subsets with this property such that this property is preserved for arbitrary unions and finite intersections, and a set is compact if it has a finite subcover for every cover with this property. A set has this property if every neighborhood of every element in the set is contained within the set. The interior of a set is the maximal subset having this property. For 10 points, name this property possessed by a set if it is the complement of a closed set.
This property is preserved by a map between Banach spaces if that map is bounded, surjective, and linear.
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