# densely defined

Given a topological space^{} $X$, we say that a map $f:Y\to X$ is densely defined if its domain $Y$ is a dense subset of $X$.

This terminology is commonly used in the of linear operators^{} with the following meaning: In a normed space $X$, a linear operator $A:\mathcal{D}(A)\subset X\to X$ is said to be densely defined if $\mathcal{D}(A)$ is a dense vector subspace of $X$.

Title | densely defined |
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Canonical name | DenselyDefined |

Date of creation | 2013-03-22 13:48:12 |

Last modified on | 2013-03-22 13:48:12 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 7 |

Author | Koro (127) |

Entry type | Definition |

Classification | msc 47A05 |

Classification | msc 54C10 |