13 Continuousdeformation of sets and curves
13.1 Continuous deformation of closed sets in ℝ2
Using some suggestive terminology we will define below, Figure 13.1 shows two dynamic closed sets A and B in the plane which move from being disjoint to meeting and then to overlapping. Would it be possible for dynamic closed sets A and B in the plane to move from being disjoint directly to overlapping, without first meeting? Such questions require a careful definition of meeting, overlapping, and continuous deformation, and the answers may depend on what kinds of sets (closed, compact, connected, etc.) are permitted.
Figure 13.1 A transition from ...
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