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I don't have a copy to check this out against but when I read your question I immediately though of Greg Bear's City at the End of Time. en.wikipedia.org/wiki/City_at_the_End_of_Time
I read this many years ago when it first came out and I must admit it's been re-read a few times since then. You might also be interested to know that there is a sequel called 'I Remember Pallahaxi'.
