Add new alias to strongly paracompact; hypo and total properties.

[Moniker1998]

In the literature, the term hypocompact seems to be used to what we refer to as strongly paracompact.

See remark to the definitions in this question, as well as my comments under the answer to it. The only reason I am not 100% sure, is that I cannot seem to find the articles online.

There are also other properties, totally hypocompact, totally metacompact and hypoLindelof which we could add in the future, but for now we could add the alias.

[prabau]

I agree it would be good to add hypocompact as alias for strongly paracompact, and mention at the same time some reference using that term. See for example https://math.stackexchange.com/questions/1124179, which confirms the two properties are the same, and the references there in the comments at the end, to choose from:

• https://zbmath.org/0058.38602 (Iséki, On hypocompact spaces)
• https://zbmath.org/0207.52704 (Greever, On some generalized compactness properties)

And before adding some of the other properties you mention, "totally paracompact" should be added, as it seems less esoteric than those to start with.
(The introduction section of https://zbmath.org/1043.54010 (John Porter, Base-paracompact spaces) has a good summary.)