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In this paper we introduce the concept of a sequence convergence of dimensional  subspaces (lines) in a normed space. We shall discuss some properties of  it. Futhermore we prove a continuity property of angles among  subspaces in  inner product spaces. Finally, the notion of limit of a sequence of dimensional  subspaces (planes) in a normed space is studied. We also obtain a result which describe how the convergent of a sequence of lines is associated to the convergent of a sequence of planes in a normed space.

continuity property of angles, inner product spaces