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Model-independent estimations for the spatial curvature of the universe not only provide a test for the fundamental assumption of the Copernican principle, but also can effectively break the degeneracy between curvature and dark-energy properties. In this paper, we propose to achieve model-independent constraints on the spatial curvature from observations of standard candles and standard clocks, without assuming any fiducial cosmology or other priors. We find that, for the popular Union2.1 observations of Type Ia supernovae (SNe Ia), the spatial curvature is constrained to be . For the latest joint light-curve analysis of SNe Ia observations, we obtain . It is suggested that these results are in excellent agreement with a spatially flat universe. Moreover, compared to other approaches aiming for model-independent estimations of spatial curvature, this method also achieves constraints with competitive precision. [ABSTRACT FROM AUTHOR]

Model-independent constraints on the spatial curvature are not only closely related to important problems, such as the evolution of the universe and properties of dark energy, but also provide a test of the validity of the fundamental Copernican principle. In this paper, with the distance sum rule in the Friedmann–Lemaître–Robertson–Walker metric, we achieve model-independent measurements of the spatial curvature from the latest type Ia supernovae and strong gravitational lensing (SGL) observations. We find that a spatially closed universe is preferred. Moreover, by considering different kinds of velocity dispersion and subsamples, we study possible factors that might affect model-independent estimations for the spatial curvature from SGL observations. It is suggested that the combination of observational data from different surveys might cause a systematic bias, and the tension between the spatially flat universe and SGL observations is alleviated when the subsample only from the Sloan Lens ACS Survey is used or a more complex treatment for the density profile of lenses is considered. [ABSTRACT FROM AUTHOR]