Pointless Topology

In mathematics, pointless topology (also called point-free or pointfree topology) is an approach to topology that avoids mentioning points. The name 'pointless topology' is due to John von Neumann. The ideas of pointless topology are closely related to mereotopologies in which regions (sets) are treated as foundational without explicit reference to underlying point sets.

Read more about Pointless TopologyGeneral Concepts, Categories of Frames and Locales, Relation To Point-set Topology

Other articles related to "pointless topology, topology":

Pointless Topology - Relation To Point-set Topology
... It is possible to translate most concepts of point-set topology into the context of locales, and prove analogous theorems ... While many important theorems in point-set topology require the axiom of choice, this is not true for some of their analogues in locale theory ... how equality between sets of open rectangles, the canonical base for the product topology, is defined equality for the topological product means the same set of points is ...
Pointlessly
... In mathematics, pointless topology (also called point-free or pointfree topology) is an approach to topology that avoids mentioning points ... The name 'pointless topology' is due to John von Neumann ... The ideas of pointless topology are closely related to mereotopologies in which regions (sets) are treated as foundational without explicit reference to underlying point sets ...

Famous quotes containing the word pointless:

    One’s condition on marijuana is always existential. One can feel the importance of each moment and how it is changing one. One feels one’s being, one becomes aware of the enormous apparatus of nothingness—the hum of a hi-fi set, the emptiness of a pointless interruption, one becomes aware of the war between each of us, how the nothingness in each of us seeks to attack the being of others, how our being in turn is attacked by the nothingness in others.
    Norman Mailer (b. 1923)