There are two different definitions of spectrum. Both are relevant in thei
own respect, but not the same.

As far as the FFT is concerned: It "sees" one cycle of a signal that migh
be periodic from minus to plus infinity. There is ideally no energy leakag
from one subcarrier to the other, including for example adjacent but unuse
frequency regions inside the same FFT.

The other definition becomes relevant when I connect a radio frequenc
spectrum analyzer (or its baseband equivalent).
Other than the FFT, it knows nothing about the cyclic assumption, and i
is not synchronized with the symbol structure.
Suddenly the spectrum looks quite messy, energy seems to leak everywhere

That is caused by the DISCONTINUITIES between symbols: At the symbo
boundary, the signal "jumps" from one instantaneous amplitude to another.
This can be expressed as multiplication of each symbol with a rectangula
window => sinc spectrum. It is completely transparent to the FFT, bu
hurts other users that aren't synchronized and can't take advantage of th
single-cycle processing.
In an implementation, an "ideal" symbol-to-symbol discontinuity from
rectangular window jams too much energy into adjacent bands, and we nee
to tame it somehow (for example filtering)

Hope that clarifies somewhat.

-Markus