Simulate a regular Turing Machine with one that cannot write blanks
To simulate a Turing machine&nbsp;$M$ that can write blanks with a Turing machine&nbsp;$M'$ that can't, just give&nbsp;$M'$ an extra character in its alphabet. Whenever $M$&nbsp;writes a blank, $M'$&nbsp;writes this new character and, whenever $M'$&nbsp;sees the blank or the new character, it does what $M$&nbsp;would do if it saw the blank.