Question

Hello,

I would like to work with 2 and 3 but step by step

awy - 2. We can define the line (R) as a product Zx (0,1), with the dictionary order. Show this is homeomorphic to R. 3. The long line (or Alexandrov line) is defined as the product of So, the minimal uncountable well-ordered set, with the interval (0,1) with the dictionary order with the smallest element deleted. Intuitively the long line consists of uncountably many copies of the interval [0,1). Show that the long line is Hausdorff.

Answer 1

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