halfgesloten

Halfgesloten is a Dutch adjective meaning partially closed or not fully closed. It can describe tangible objects, such as a door that is not fully shut, a jar with its lid left ajar, or a window that is slightly opened. In everyday language it often conveys the idea of an opening that is present but not completely covered or sealed.

In mathematics, halfgesloten refers to a half-closed interval, also called a half-open interval. This is a set of real numbers that includes one endpoint but excludes the other, for example [a, b) or (a, b]. In Dutch mathematical texts, halfopen is a common synonym for the same concept, but halfgesloten is also understood. A halfgesloten interval is closed on one side and open on the other, which gives it distinct properties from fully closed or fully open intervals.

Topologically, a halfgesloten interval in the real numbers is neither open nor closed in the standard topology. It is bounded and connected, but it is not closed because, for instance, the limit point b is not contained in [a, b). Consequently, [a, b) is not compact in R, since compact subsets of R must be closed and bounded.

Beyond mathematics, the term halfgesloten can appear in descriptions of physical objects or mechanisms that are only partially closed, indicating a state between fully closed and fully open. The exact nuance may vary with context, but the core idea remains: a partial closure leaving an opening.