Help me identify this collection of Sci-fi stories

When I was in high school, I read a collection of sci-fi stories based around the end of the world/universe/etc.

Unfortunatly, I can’t remember the names of any stores other then “At the Core” by Larry Niven. I can remember some plot descriptions and authors.

-One was a story by Ben Bova(I think), with a human, the last survivor of an intersteller war that mankind lost, being chased across the universe by the enemy, determined to wipe out humanity completely. Due to time dilation, the human manages to survive to the end of the universe, and points this out to his pursuers.

-One may or may not have been “The Last Trump” by Issac Asimov. I was sure it was, but the description I read doesn’t quite match what I recall reading.

-One invovled a gathering of aliens in the far future, with representatives trying to present the most novel thing to relieve galatic ennui. The winner is a recording of the universe dying the last time, and as it is about to do again.

Do any of these ring a bell?

Could the collection be Catastrophes!, which contains “At the Core”, "The Last Trump, and a Ben Bova story called “Stars, Won’t You Hide Me?”

That is indeed Catastrophes!, edited by Isaac Asimov, Martin H. Greenberg and Charles G. Waugh (1981). The link is a picture I took of the cover. Great book. Excellent stories.

Here’s how to answer questions like this where you remember a specific story and you want to find the anthology: First, go to the Internet Speculative Fiction Database:

You don’t have to store that URL if you don’t want to. Just Google on “Internet Speculation Fiction Database” and it’s right at the top of the list. You can search within that database on either author or story title. It will give you a list of every place that the story has appeared. At least, it claims to list all the places where it appears. It probably misses some, but it’s close enough to being complete that it’s very useful.

That’s it. Thanks. I really appreciate it.