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  "body": "\n## Summary\n\nAn FK-space is a [[sequence space|XYTN19EPF2]] with a complete metrizable locally convex topology in which each coordinate $x \\mapsto x_n$ is continuous.\nThe letters stand for Fréchet and the German word Koordinate.\nFK-spaces are the main tool of the functional analytic approach to summability: the domain of a matrix summability method is an FK-space.\nA sequence space carries at most one FK topology, and inclusions between FK-spaces are automatically continuous.\n\n## Explanations\n\n### L1 human\n\nA sequence space becomes much easier to study once it has a good notion of distance.\nIn an FK-space the distance is complete, like the distance on the real line, and it controls each term of a sequence.\nSo if two sequences are close in the space, then their first terms are close, their second terms are close, and so on.\nThe spaces $\\ell^p$ with their usual norms are FK-spaces, and so is the space of all sequences with the topology of termwise convergence.\n",
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