no, a divided cell is where the electrodes would be in different vessels or buckets in your case with an ion bridge between them.

Ah, sort of like with galvanic cells or electrochemical cells. Got it.

Electrolysis of water could be carried in in undivided cell having stainless anode and cathode and dil sulphuric acid as electrolyte. The electrodes will be of concentric cylindrical design. The oxygen and hydrogen can be collected separately .

In a divided membrane cell, KOH (6M, 80'C) is used as electrolyte, both as anolyte and catholyte. Anode and cathode compartments are separated by a cation exchange membrane.Oxygen and hydrogen gases are collected separately form anode and cathode compartments respectively. Anode may be Nickel/or oxide coated Nickel and cathode is Nickel or coated nickel. Membrane is perfluro sulfonic acid based membrane (Nafion 424 or Nafion 900 series or Nafion 2000)

The process by which we generate hydrogen (and oxygen) from water is called electrolysis. The word "lysis" means to dissolve or break apart, so the word "electrolysis" literally means to break something apart using electricity.

well, that was completely redundant to the thread. its pretty clear the OP knows it is called electrolysis.

Ok so are you guys saying I can use epson salt to put into water, put a charge to it say with a battery charger to referbish a dead led acid battery ?