Instants, monads, closed and open intervals, etc. are terms that have been defined for different views of temporal “works.” These definitions are particular to the world-view being described and may, in fact, be different for different world-views and systems of thought. I ask, “Under whose world-view are you attempting to answer the question?”
I have a world-view that is described in Natural Logic of Space and Time (NL) which is a logic system and parallel-concurrent algebra suitable for DES (discrete event systems) process specification and control. For every condition that occurs there is an event that caused it. So, in my view and system, every meaningful interval (at which a condition significant to the process exists) has a causative event at either end. Meaningful, in this regard, is one that constructively participates in and is integral to the process.