yhteydellinen

Yhteydellinen is a Finnish word that translates to "connected" or "contiguous" in English. It is often used in mathematics and other fields to describe a property of a set or space.

In topology, a set is called yhteydellinen if it cannot be partitioned into two or more non-empty, disjoint open sets. Intuitively, a connected set is one where you can get from any point in the set to any other point in the set by moving along a continuous path within the set. A space that is yhteydellinen is considered to be in one piece.

For example, a line segment in Euclidean space is yhteydellinen. If you pick any two points on the segment, you can always draw a straight line between them that lies entirely within the segment. However, a set consisting of two separate points would not be yhteydellinen, as there is no way to move from one point to the other without leaving the set.

The concept of yhteydellinen is fundamental in many areas of mathematics, including analysis, differential geometry, and algebraic topology. It plays a crucial role in understanding the structure and properties of various mathematical objects. The opposite of being yhteydellinen is being disconnected, meaning the set can be divided into separate parts.