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2. Projection (set theory) - Wikipedia

   en.wikipedia.org/wiki/Projection_(set_theory)

   Projection (mathematics) – Mapping equal to its square under mapping composition; Projection (measure theory) Projection (linear algebra) – Idempotent linear transformation from a vector space to itself; Projection (relational algebra) – Operation that restricts a relation to a specified set of attributes

3. Map (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Map_(mathematics)

   Maps of certain kinds have been given specific names. These include homomorphisms in algebra, isometries in geometry, operators in analysis and representations in group theory. [2] In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems. A partial map is a partial function.

4. Category of sets - Wikipedia

   en.wikipedia.org/wiki/Category_of_sets

   The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps. The empty set serves as the initial object in Set with empty functions as morphisms. Every singleton is a terminal object, with the functions mapping all elements of the source sets to the single target element ...

5. Exponential object - Wikipedia

   en.wikipedia.org/wiki/Exponential_object

   In mathematics, specifically in category theory, an exponential object or map object is the categorical generalization of a function space in set theory. Categories with all finite products and exponential objects are called cartesian closed categories. Categories (such as subcategories of Top) without adjoined products may still have an ...

6. List of alternative set theories - Wikipedia

   en.wikipedia.org/wiki/List_of_alternative_set...

   In mathematical logic, an alternative set theory is any of the alternative mathematical approaches to the concept of set and any alternative to the de facto standard set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory.

7. Axiom schema of replacement - Wikipedia

   en.wikipedia.org/wiki/Axiom_schema_of_replacement

   Indeed, Zermelo set theory (Z) already can interpret second-order arithmetic and much of type theory in finite types, which in turn are sufficient to formalize the bulk of mathematics. Although the axiom schema of replacement is a standard axiom in set theory today, it is often omitted from systems of type theory and foundation systems in topos ...

8. Set-theoretic topology - Wikipedia

   en.wikipedia.org/wiki/Set-theoretic_topology

   Cardinal functions are widely used in topology as a tool for describing various topological properties. [4] [5] Below are some examples.(Note: some authors, arguing that "there are no finite cardinal numbers in general topology", [6] prefer to define the cardinal functions listed below so that they never take on finite cardinal numbers as values; this requires modifying some of the definitions ...

9. Category:Graphical concepts in set theory - Wikipedia

   en.wikipedia.org/wiki/Category:Graphical...

   Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Graphical concepts in set theory" The following 5 pages are in this ...