In mathematics — specifically, in operator theory — a densely defined operator or partially defined operator is a type of partially defined function; in a topological sense, it is a linear operator that is defined "almost everywhere". Densely defined operators often arise in functional analysis as operations that one would like to apply to a larger class of objects than those for which they a priori "make sense".
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Famous quotes containing the words densely and/or defined:
“I keep having the same experience and keep resisting it every time. I do not want to believe it although it is palpable: the great majority of people lacks an intellectual conscience. Indeed, it has often seemed to me as if anyone calling for an intellectual conscience were as lonely in the most densely populated cities as if he were in a desert.”
—Friedrich Nietzsche (1844–1900)
“Why is it so difficult to see the lesbian—even when she is there, quite plainly, in front of us? In part because she has been “ghosted”Mor made to seem invisible—by culture itself.... Once the lesbian has been defined as ghostly—the better to drain her of any sensual or moral authority—she can then be exorcised.”
—Terry Castle, U.S. lesbian author. The Apparitional Lesbian, ch. 1 (1993)