the essential relationship between the two is that the "you of today" shares the memories of "you of yesterday"

except that we forget most of them, and that our memories of the same event change in time, and often are completely fictional.

Good point. The description I gave so far is just a first approximation. In truth, memory is far from ideal. However if we assign weight to memories by their potential impact on our thinking and decision making then I think we would get that most of the memories are preserved, at least on short time scales. So, from my point of view, the "you of today" is only a partial continuation of the "you of yesterday". However it doesn't essentially changing the construction of the Hypermind. It is possible to refine the hypothesis by stating that for every two "pieces of knowledge" a and b, there exists a "moment of consciousness" C s.t. C contains a and b.

"The Asymptote has property P" is "For any A there is B > A s.t. for any C > B, C has property P"

That's a rather non-standard definition. If anything, it's close to monotonicity than to accumulation. If you mean the limit point, then you ought to define what you mean by a neighborhood.

Actually I overcomplicated the definition. The definition should read "Exists A s.t. for any B > A, B has property P". The neighbourhoods are sets of the form {B | B > A}. This form of the definition implies the previous form using the assumption that for any A, B there is C > A, B.