The Apple ][ we had had a 64k address space, true. But it was bank switched. Main memory was 60k, as I recall, but the top 4k had an OS function to select an additional 60k that would map into the low-order 60k. So you had a high 4k permanent bank and two low switched banks of 60k each.
If you stuck to BASIC you never knew this was going on, and maybe it was only the later machines that did this. But us 6502 hackers knew it. A total of 124k.
It was many years ago; I think it was the top 4k but it might have been the top 8k. I thought it was so neat that Apple was using address lines to bank switch.