On complete topological spaces

@article{Neumann1935OnCT,
  title={On complete topological spaces},
  author={J. Neumann},
  journal={Transactions of the American Mathematical Society},
  year={1935},
  volume={37},
  pages={1-20}
}
  • J. Neumann
  • Published 1935
  • Mathematics
  • Transactions of the American Mathematical Society
  • DEFINITION I. If M is a space in which there is defined a metric dist (f, g) satisfying the usual postulates for distance ([1], p. 94), then a sequence F: fl, f2, * * * is fundamental if, for every 3>0, there exists an n = nli (3) such that m, n > ni imply dist (fn, f,) 0, there exists an n2 = n2(8) such that n > n2 implies dist (f, f,) < 8. M is complete if every fundamental sequence is convergent. 
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