In quantum many-body systems, quantum phase transitions are among the most fascinating phenomena. In general, quantum phase transitions can be classified into two categories: (1) conventional and (2) topological. Conventional quantum phase transitions are the quantum generalization of thermal phase transitions. Similar to their classical counterparts, they are characterized by spontaneous symmetry breaking. A topological phase transition doesn’t have any symmetry breaking. Instead, it is the singular point where the quantum wavefunction changes its topology. In comparison to conventional phase transitions, our knowledge on topological phase transitions are much more limited. In fact, we don’t even have a general recipe yet to determine whether two quantum states have the same topology or not, and a complete and constraint-free classification of topological states is still absent. As a step toward this ultimate goal, we prove a general theorem: for two arbitrary quantum states, as long as the inner product between the two wavefunctions is nonzero, there exists an adiabatic path connecting the two quantum states. This theorem can be utilized to study all topological phase transitions in non-interacting or weakly-correlated systems, as well as certain strongly-correlated systems. For topological phase transitions, our theorem implies that two quantum states with finite wavefunction inner product must belong to the same quantum phase and thus have exactly the same topological structure. We will further discussion how this theorem can help us understand the classification of topological states, as well as its implications in experiments.