Explained that the real interval (-1,1) is homeomorphic to the real line.
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Proved that "connectedness" is a topological property, and used this property to prove that the real line is NOT homeomorphic to the real plane.
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Finished up by justifying the use of the term "compact space" in favour of "finite space" or "bounded space", and explained one reason why we'd like to prove that "compactness" is a topological property. The precise definition of "compactness" will be given in the next lecture.