La geometria intesa come studio delle invarianze e permanenze delle figure.
vedi schema.
topologia; topologia uniforme (omogeneo); proiettiva; affine; simile; rigida.
Per l'aspetto vettoriale vanno considerati gli spazi vettoriali.
Lo spazio vettoriale-topologico guarda entrambi gli aspetti.
mathpath.org/concepts/geometries.htm
If you cleave the hearth of one drop of water
a hundred pure oceans emerge from it.
(Mahmud Shabistari, Gulshan-i-raz)
We have decided to contribute to the volume of the IPM lectures on
noncommutative geometry a text that collects a list of examples of
noncommutative spaces. As the quote of the Sufi poet here above suggests, it is
often better to approach a new subject by analyzing specific examples rather
than presenting the general theory. We hope that the diversity of examples the
readers will encounter in this text will suffice to convince them of the fact
that noncommutative geometry is a very rich field in rapid evolution, full of
interesting and yet unexplored landscapes.
ix Geometria analitica, o cartesiana.