We complete the proof of connectedness of [a,b]. We investigate whether some subsets of R2, the plane, especially conic sections, are connected or not. On the way we prove that the continuous image of a connected set is connected.
Timestamp provided by Ishwarya.
0:00 Introduction
1:41 Completion of proof of connectedness of [a,b]
5:02 Rectangular Hyperbola is not connected
10:46 Non degenerate Conics
11:28 Theorem: Continuous image of connected set is connected
15:42 Mantra to deal with inverse images
15:54 Circle in R^2 is connected
17:56 Ellipse in R^2 is connected
18:33 Parabola in R^2 is connected
20:25 About degenerate cases
21:10 Summary
22:39 Two lines x=a and x=b , (a and b different) are not connected
24:42 y=ax+b is connected
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