on we define an order topology (lexicographic order) as follow: if or ( & ).

Is this topology equivalent to the standard topology? if not, which topology is finer?(give an example of an open set in one but not in the other)?

thanks :)

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- Mar 9th 2011, 01:32 AMaharonidanOrder Topology vs. the standard one?
on we define an order topology (lexicographic order) as follow: if or ( & ).

Is this topology equivalent to the standard topology? if not, which topology is finer?(give an example of an open set in one but not in the other)?

thanks :) - Mar 9th 2011, 02:16 AMtonio
- Mar 9th 2011, 02:43 AMaharonidan
I wasn't clear enough. if (X,<) is a partial order set, then all (a,b) a<b U (-infinity,infinity) is a base of a topology on X.

now I need to compare this topology with the Euclidean one.

any help or hint is appreciated