Skip to main content
MathOverflow

Return to Question

replaced http://mathoverflow.net/ with https://mathoverflow.net/
Source Link
Community Bot
Community Bot
  • 1
  • 2
  • 3

Motivated by this questionquestion we ask:

Up to homeomorphism, are there only a finite number of connected locally compact hausdorff topological space $X$ such that $X$ has an open set $U$ homeomorphic to $\mathbb{R}$ such that $X-U$ is homeomorphic to $\mathbb{R}$, too? (Note that there is only one disconnected possibility, so we add connectedness assumption)

Motivated by this question we ask:

Up to homeomorphism, are there only a finite number of connected locally compact hausdorff topological space $X$ such that $X$ has an open set $U$ homeomorphic to $\mathbb{R}$ such that $X-U$ is homeomorphic to $\mathbb{R}$, too? (Note that there is only one disconnected possibility, so we add connectedness assumption)

Motivated by this question we ask:

Up to homeomorphism, are there only a finite number of connected locally compact hausdorff topological space $X$ such that $X$ has an open set $U$ homeomorphic to $\mathbb{R}$ such that $X-U$ is homeomorphic to $\mathbb{R}$, too? (Note that there is only one disconnected possibility, so we add connectedness assumption)

Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

A question in general topology

Motivated by this question we ask:

Up to homeomorphism, are there only a finite number of connected locally compact hausdorff topological space $X$ such that $X$ has an open set $U$ homeomorphic to $\mathbb{R}$ such that $X-U$ is homeomorphic to $\mathbb{R}$, too? (Note that there is only one disconnected possibility, so we add connectedness assumption)