Semiosphere, a notion developed by Jurij Lotman starting in 1984, provides the means to rethink narrative world within the framework of cultural semiotics on the basis of concepts such as binary relations, asymmetry, heterogeneity, border, translatability, etc. The border is crucial in the generation of semiosphere, as it is in the various types of narrative, and thus in the nature of the narrative world. Text without subject (where the border is not crossed, as in origin myths) is distinguished from text with subject (where the story is triggered by the violation of a taboo, for example). To put narrative world as conceived according to the principles of semiosphere into perspective, the notions of storyworld (David Herman) and eventfulness (Wolf Schmid) are examined. Storyworld is a mental construction in the reader’s mind; eventfulness focuses on the gradualness of the narrative event in context by taking account of the degree of such features as the relevance or unpredictability of changes of state as perceived by the character and the reader.