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To control particles to fly inside the limited search space and deal with the problems of slow search speed and premature convergence of particle swarm optimization algorithm, this paper applies the theory of topology, and proposed a quotient space-based boundary condition named QsaBC by using the properties of quotient space and homeomorphism. In QsaBC, Search space-zoomed factor and Attractor are introduced according to the dynamic behavior and stability of particles, which not only reduce the subjective interference and enforce the capability of global search, but also enhance the power of local search and escaping from an inferior local optimum. Four CEC'2008 benchmark functions are selected to evaluate the performance of QsaBC. Comparative experiments show that QsaBC can achieve the satisfactory optimization solution with fast convergence speed. Furthermore, QsaBC is more effective with errant particles, and has easier calculation and better robustness than other methods.