Grammar detail: あく, あける, ひらく, しめる, しまる, とじる etc.

The first important distinction is between the transitive and intransitive forms. Transitive forms take an object: you 'open a door', whereas intransitive do not: 'the view opened before us'. As in English, each of these forms however, can be used both transitively and intransitively, so this distinction is not enough. However, in general あける and ひらく are used transitively, whereas あく is usually intransitive.

The next distinction is to do with the nature of what is being opened. The important issue here is

くうかん

空間

(physical space). When the action in question joins, creates or modifies physical spaces, both ひらく and あける can be used. However, opening a book, an umbrella does not affect 'space' in the same way, and あける would be the natural choice.

The final distinction is to do with the specific subject matter. Depending on the precise context, specific terms are acceptable or not, or carry slightly different meanings. For example, while ひらく and あける could both be used to mean 'open a business', ひらく would tend to refer to the founding of the business, whereas あける would refer to opening for the day. Additionally, the terms might be written with different kanji. For example, 開く tends to be used for opening of doors and windows, 空く tends to be used for opening up of vacancies, and 明く tends to be used for periods of time.

In the same way とじる, しめる and しまる all mean 'to close'. しめる and とじる are transitive, whereas しまる is intransitive.