# why does LSPACE(log space) complexity class exist but not logtime?

I noticed that in complexity classes, logspace class is defined but there is no logtime.

I was wondering how is that possible?

Normally, I would expect the opposite, It is possible to do a search query in an ordered list in time less than the time of iterating over all items (==> Logtime?). However you can't store a list in of size n in log(n) space...

So how come Logspace exists but not logtime? there's obviously something wrong with my reasoning.

Algorithms running in $$o(n)$$ time on random-access machines are known as sublinear time algorithms. Such algorithms also abound in the area of data structures.