This space, which is not second countable, is formed from the cartesian product of ω1 with [0,1).
George Bergman constructed a p-adic analogue of this space. This space fails to satisfy the Lindelöf condition and does not possess a countable dense subset; moreover, despite the fact that this space is locally compact, it is not paracompact. This space, which is not second countable, is formed from the cartesian product of ω1 with [0,1). Any open interval (a,b) of this space is homeomorphic to the interval (0,1) in the reals, but the entire space is not homeomorphic to any subset of any   Rn. For ten points, identify this one- dimensional manifold locally homeomorphic to the reals and formed from an uncountable number of half-open intervals.
George Bergman constructed a p-adic analogue of this space. This space fails to satisfy the Lindelöf condition and does not possess a countable dense subset; moreover, despite the fact that this space is locally compact, it is not paracompact.
long line [accept Alexandro  line or long ray]