S60: homogeneity, cut points and more

[pzjp]

A few more missing traits for Pointed rational extension of R:

• Meager (resolving also Baire)
• Locally metrizable
• Homogeneity (see mathse:5013911)
• no fixed point property
• Perfect
• not sigma-connected
• Cut point space

Then P28 and P46 are redundant. Should I remove them simultaneouslty?

[prabau]

FYI, several of the previously asserted traits were just referring to the "General Reference Chart" at the end of Steen & Seebach. Not necessarily to be done in this PR, but we'd like to replace this at some point with a proper justification. (There have even been cases of a few errors in that table.)

[prabau]

And yes, it's fine to do the cleanup of some of the redundant traits at the same time.

[pzjp]

I've noticed those "general reference chart" entries and was actually thinking that these should be explained further.
For this PR the cleanup seems enough, though.

[prabau]

P205 (cut point space): We should also mention that $X$ is connected, which is part of the definition of cut point space.

Now, P36 (connected) should be a consequence of P205, so what we should do is add the reasoning for connected to P205 and remove the P36 trait file, which is redundant. (That also avoid circular reasoning.)

The current reasoning for connected refers to item 8 of S&S example 68. But that's a confusing justification for it. Instead, it should refer to item 4 of that example (which is what item 8 implicitly uses to show something else).

Summary: add something like the following to P205:

$X$ is {P36}: see item #4 for space #68 in {{doi:10.1007/978-1-4612-6290-9_6}}.