Talk:Relationship between Component Types

Utterly false claims
Let $X = \{0\}\times [0,1] \cup \{(x,\sin \frac 1 x): x > 0 \}$ have the subspace topology as a subspace of $\R^2$.

Then $X$ is connected, but not path connected, as is well known.

Let $C$ be the path component of $(0,0)$.

Then $C$ is NOT a component of $X$, because $C ≠ X$ and the only component of $X$ is $X$. Every single other statement on the page is wrong for similar reasons. If you want to talk about the relationship between sets of arc components, path components, etc., then you need to replace "is a subset of" with "is a refinement of" throughout. --Dfeuer (talk) 22:58, 7 June 2013 (UTC)


 * I looked at the relevant section of Steen and Seebach. Their presentation is not exactly clear, but in context, they mean not that the set of components is a subset of the set of quasicomponents (etc.) but rather that each component is a subset of a quasicomponent (etc.). --Dfeuer (talk) 00:19, 8 June 2013 (UTC)


 * I know you're always right, because you're so clever, but so that the rest of us subhuman neanderthal muggles can catch up with the quicksilver brilliance of your etheric transcendence, it is best to write an explanation as to why you are right, rather than just change stuff with a dismissive comment.
 * In this case, all that had happened was that OP had confused "path" with "path component", etc. One admits that when one gets older one's grasp of vocabulary slips and incorrect words get substituted for others, but please try and point out the arse-brained nature of others with a little more tact and diplomacy. --prime mover (talk) 05:11, 8 June 2013 (UTC)