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Results tagged with order-theory
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user 37103
2
votes
Accepted
Is the interval topology of $(\mathbb{N}^\mathbb{N}, \leq^*)$ connected?
I claim that this topology has the stronger property of being hyperconnected, i.e., the intersection of any two nonempty open sets is nonempty.
Indeed, any open set contains a set of the form
$$ U=\ …
- 5,169
1
vote
Accepted
Interval topology on $(\mathbb{N}^\mathbb{N},\leq^*)$
In view of the answer to this question, the answer is no, for $\tau_i$ is connected, but $\tau$ is not.
- 5,169