- #1
kent davidge
- 933
- 56
I want to show that ##\mathbb{R}## is disconnected with the subspace topology. For this I considered that ##\mathbb{R} = \lim_{\delta n \longrightarrow 0 } (-\infty, n] \cup [n+\delta n, \infty)## and of course the intersection of these two open sets is empty.
What I'm not sure is about the usage of limit here. Is this ok? I personally think it's ok, because I'm using limit only for saying that ##\delta n > 0## but that ##n+\delta n## should be the closest possible real number of ##n##...
What I'm not sure is about the usage of limit here. Is this ok? I personally think it's ok, because I'm using limit only for saying that ##\delta n > 0## but that ##n+\delta n## should be the closest possible real number of ##n##...