Fundamental properties of epsilon-connected sets

摘要

In this paper, we establish and discuss basic properties of epsilon-connected sets embedded in an arbitrary complete space. These properties are used to establish that X is epsilon-connected for all epsilon > 0 if, and only if, X is connected in the original sense of Cantor [Math. Ann. 23 (1884) 453]. Such sets are "virtually connected" in a finite precision machine and in some circumstances can be used as efficient estimators of connected geometric figures. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 5]