Thinly slice the cabbage and bell pepper. Shred the carrot. Place the vegetables in a large bowl and mix well.
Transfer the cabbage mix into a glass jar, packing tightly.
In a small saucepan, bring the water, sugar, and salt to a boil. Remove the pan from the heat and add the vinegar and olive oil. Give it a stir, and pour the marinade into the jar with the cabbage.
Cool completely and transfer it to the fridge. Allow at least 12 hours to pickle. Serve.
