Inconsistent TypeError: cannot serialize '_io.TextIOWrapper' object

the problem is that you should avoid same names for different objects, in your case should help

• changing function name from f to function (or another name different from f)

  cell 1

  from time import time
  from multiprocessing import Pool
  import portalocker
  
  
  def function(*args):
      while time() < start + 1:
          pass
      with open('portalocker_test.txt', 'a') as f:
          portalocker.lock(f, portalocker.LOCK_EX)
          f.write(f'{time()}\n')
  

  cell 2

  start = time()
  with Pool(4) as p:
      p.map(function, range(4))
  

or

• renaming file objects obtained with open from f to file (or another name different from f):

  cell 1

  from time import time
  from multiprocessing import Pool
  import portalocker
  
  
  def f(*args):
      while time() < start + 1:
          pass
      with open('portalocker_test.txt', 'a') as file:
          portalocker.lock(file, portalocker.LOCK_EX)
          file.write(f'{time()}\n')
  

  cell 3

  with open('portalocker_test.txt', 'r') as file:
      for line in file:
          print(line, end='')
  

or both