pretopology

Noun

Meaning

(mathematics) The field of study of pretopological spaces (in plural for different prespaces).

(mathematics) A filter subset or a preclosure operator which acts as a distinct prespace (pre-topological space).

Examples

If J is the topology defined by a pretopology, and if u commutes with fibered products, then u is continuous if and only if it sends covering sieves to covering sieves and if and only if it sends covering families to covering families. Source: Internet

The Zariski topology on Sch is generated by the pretopology whose covering families are jointly surjective families of scheme-theoretic open immersions. Source: Internet

The indiscrete topology is also known as the biggest or chaotic topology, and it is generated by the pretopology which has only isomorphisms for covering families. Source: Internet

If the collection of all covering families satisfies certain axioms, then we say that they form a Grothendieck pretopology. Source: Internet

We can also define this topology using the same pretopology we used above. Source: Internet

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