Banach's Continuous Inverse Theorem and Closed Graph Theorem

@article{Sakurai2012BanachsCI,
  title={Banach's Continuous Inverse Theorem and Closed Graph Theorem},
  author={Hideki Sakurai and Hiroyuki Okazaki and Yasunari Shidama},
  journal={Formalized Mathematics},
  year={2012},
  volume={20},
  pages={271-274}
}
The terminology and notation used here have been introduced in the following articles: [3], [4], [2], [15], [11], [14], [1], [5], [13], [12], [19], [20], [16], [7], [17], [8], [18], [9], and [6]. Let X, Y be non empty normed structures, let x be a point of X, and let y be a point of Y . Then 〈x, y〉 is a point of X × Y. Let X, Y be non empty normed structures, let s1 be a sequence of X, and let s2 be a sequence of Y . Then 〈s1, s2〉 is a sequence of X × Y. We now state several propositions: (1… CONTINUE READING