Could a stairway to the basement be open to the first floor?

Could a stairway to the basement be open to the first floor?
Sure, but it depends on framing and furnace locations. A door to the basement stairway is a must for safety issues in most cases. Is gas furnace in basement? Describe the open flooring that you want. Nm

That's pretty much standard where I live, in the Midwest. Open doorways to the basement, that is. However, keep in mind, we almost always finish our basements, so they are constructed that way. It really depends on your type of basement. If it just for utilities and/or storage, I'd want a door. If you have bedrooms and bathrooms downstairs, open is nice.