Moniker1998

https://math.stackexchange.com/a/5072215/476484 I've also constructed a locally compact Hausdorff space for any possible triples of cardinals for which a space with given amount of quasi-components, components and path-components exists.

> Cool! I wonder how to express that in pi-base properties. I don't think it can be 😛 but I still wanted to share, since I've noticed its probably your...

> It would be ok to add these trivial results if it would make redundant some asserted traits of spaces. > > Without that, I am not sure it's worth...

This particular theorem doesn't need to be added, see [here](https://topology.pi-base.org/spaces?q=Hausdorff+%2B+Paracompact+%2B+Pseudocompact+%2B+%7ECompact). You didn't search correctly, that's why nothing came up. However, the search for a [paracompact pseudocompact space which is not...

I don't understand OP's current argument, but Fully normal + pseudocompact => compact seems like it should be able to be proven the same way

Note that there was #778 where we discussed the property Feeble compact, equivalent to pseudocompactness for Tychonoff spaces. paracompact + feebly compact iff compact

I thought you didn't want to add this property

The more the merrier

Let me expand a little on why I think this property should be added. 1. We already have other analogous properties of such type. Indeed, Hausdorff and functionally Hausdorff spaces...

I don't see a problem in some properties going through complicated theorems. Sometimes an intermediary implication $A\implies B\implies C$ is a non-trivial theorem while $A\implies C$ is quite trivial, too....