leftclosed

The term "leftclosed" is primarily used in mathematics, specifically in the context of intervals and topology. An interval is said to be leftclosed if it includes its left endpoint. For example, the interval [a, b] is leftclosed and also rightclosed, meaning it includes both its endpoints a and b. In contrast, an interval like (a, b] is rightclosed but not leftclosed, as it excludes its left endpoint a. Similarly, an interval (a, b) is neither leftclosed nor rightclosed.

In topology, the concept extends to sets and neighborhoods. A set can be considered "leftclosed" in certain contexts, implying that the boundary point on the left side of a region is part of that region. This distinction is important when defining open or closed sets, and in analyzing the properties of topological spaces, particularly when dealing with order structures or specific types of spaces like intervals on the real line. The opposite of leftclosed is typically referred to as leftopen.