Where does closed collide?

In topology a closed set is one whose complement is open, equivalently a set that contains all of its limit points, so that no sequence inside it can converge to a point left outside. Munkres's Topology defines closed sets this way and builds closure, boundary, and continuity on the notion. The referent is a precise property of a set within a topological space, defined by containment of limit points, and it is unrelated to a system that exchanges no matter or an economy without foreign trade apart from the general idea of being shut off.[1]

Unit

A set equal to its own closure (contains all limit points)

Recovery means

Not applicable

Measured by

Verified by showing the complement is open or that every limit point of the set lies in the set

In thermodynamics a closed system is one whose boundary allows energy to cross, as heat or work, but across which no mass flows, in contrast with an open system that exchanges matter and an isolated system that exchanges neither. Çengel and Boles's Thermodynamics: An Engineering Approach builds its analysis of control masses on this definition. The referent is a physical system defined by what may cross its boundary, a concrete modelling choice about mass and energy flow, distinct from a topological set or a national economy except for the shared meaning of being closed off to something.[2]

Unit

A system boundary that passes energy but not mass

Recovery means

Not applicable

Measured by

Identified by accounting for energy transfers across a boundary that no mass crosses

In economics a closed economy is one that does not trade with the rest of the world, so that it neither exports nor imports and its output equals domestic spending, used as a simplifying baseline against the open economy. Mankiw's Principles of Economics introduces the closed economy to derive national saving and investment before adding international flows. The referent is a modelling assumption about an economy's external transactions, an analytic idealisation unrelated to a topological set or a thermodynamic boundary beyond the common notion of being sealed from outside exchange.[3]

Unit

An economy with no cross-border flows of goods or capital

Recovery means

Not applicable

Measured by

Treated as an accounting identity in which output equals domestic consumption, investment, and government spending