olemus
normeeritud ruum, mis normi abil defineeritud kauguse
$d(x,y) = ||x - y||$ mõttes on täielik meetriline ruum
= a complete normed vector space in mathematical analysis

näiteid
= $n$-mõõtmeline Eukleidiline vektorruum $\mathbb{R}^n$, milles
vektori $x=(x_1,x_2,\ldots,x_n)$ norm
on $||x||_p = \sqrt[p]{|x_1|^p + |x_2|^p + \ldots + |x_n|^p}$
= seost $\sum_i |x_i|^p<\infty$ rahuldavate
reaalarvujadade $x=(x_0,x_1, x_2, \ldots )$
vektorruum normiga \(||x||_p = \sqrt[p]{\sum_i |xi|^p}\)

ülevaateid
https://www.techopedia.com/definition/17852/banach-space
https://en.wikipedia.org/wiki/Banach_space
https://encyclopediaofmath.org/wiki/Banach_space
https://www.math.ucdavis.edu/~hunter/book/ch5.pdf
http://www.ma.huji.ac.il/~razk/iWeb/My_Site/Teaching_files/Banach.pdf