Analysis MOC

Seminormed vector space

A seminormed vector space is a Vector space over a Subfield of equipped with a seminorm , a weakening of a norm satisfying the following conditions for any and vec

1. Absolute homogeneity:
2. Triangle inequality:

whence follows

3. Nonnegativity:

By strengthening nonnegativity to positive-definiteness the seminorm becomes a full norm.

Properties

1. A seminorm induces a normed quotient

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