1
I left the house without to eat breakfast.
I left the house without eating breakfast.
Without is a preposition. When a verb follows a preposition, use the -ing form, not to + verb: ‘She went to bed without saying goodbye.’
2
It was raining, but I went out without umbrella.
It was raining, but I went out without an umbrella.
Use a/an after without when the next word is a singular countable noun: ‘without a coat’, ‘without an umbrella’.