Flagellate. Flail.


Flatulence?

Flatware!

(Shit. There's that damn "submit" button again.)

Fabulous? Freakin?

;)

In functional analysis, an F-space is a vector space *V over the real or complex numbers together with a metric: d : V × V → R so that

1. Scalar multiplication in V is continuous with respect to 'd' and the standard metric on 'R' or 'C'.
2. Addition in 'V' is continuous with respect to 'd'.
3. The metric is translation-invariant, i.e. d(x+a, y+a) = d(x, y) for all x, y and a in V
4. The metric space (V, d) IS complete

Various authors refer to these spaces "Fréchet spaces", but in Wikipedia, the term Fréchet space is reserved for locally convex F-spaces.

Clearly, all Banach spaces and Fréchet spaces are F-spaces. The Lp spaces for 0 < p < 1 are examples of F-spaces which are not Fréchet spaces.

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