Answer by Brian M. Scott for Proving statements about homeomorphisms are...
Proving a ring of implications is often the most efficient way to proceed, and it works fine here, but I’d probably proceed a bit differently with this result. In all three conditions the function in...
View ArticleAnswer by Gregory Nisbet for Proving statements about homeomorphisms are...
The open map and closed map conditions are very similar to each other, so it makes sense to prove both at the same time give $(a)$ as a hypothesis. When proving $a$ given either $(b)$ or $(c)$ it makes...
View ArticleAnswer by Rob Arthan for Proving statements about homeomorphisms are equivalent
If you want to show that $\phi_1, \ldots, \phi_n$ are equivalent, you need to prove enough of the statements $\eta_{ij} \equiv \phi_i \Rightarrow \phi_j$, so that the $\eta_{ij}$ viewed as edges on a...
View ArticleProving statements about homeomorphisms are equivalent
I am trying to prove the following equivalences. What is a good way to prove statements in a chain of statements like this are equivalent. By both taking the easiest, most efficient route for proving...
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