Abstract. If X is a complete metric space, the collection of all non-empty compact subsets of X forms a complete metric space (H(X),h), where h is the Hausdorff metric. In this paper we explore some of the geometry of the space H(R^n). Specifically, we concentrate on understanding lines in H(R). In particular, we show that for any two points A, B in H(R^n), there exist infinitely many points on the line joining A and B. We characterize some points on the lines formed using closed and bounded intervals of R and show that two distinct lines in H(R) can intersect in infinitely many points.
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Furman University Electronic Journal of Undergraduate Mathematics