To border upon; be next to; abut on; be adjacent to.
To touch by means of a mutual border, edge or end; to border on; to lie adjacent (to); to be contiguous (said of an area of land)
To lean against on one end; to end on, of a part of a building or wall.
To be in contact or connection with.
To extend an algebraic object (e.g. a field, a ring, etc.) by adding to it (an element not belonging to it) and all finite power series of (the element).