pointless topology, also called point-free topology (or pointfree topology) or topology without points and locale theory, is an approach to topology that...

Occasionally, one needs to use the tools of topology but a "set of points" is not available. In pointless topology one considers instead the lattice of open...

general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It...

subspace – In mathematics, vector subspace Pointless topology Quasitopological space – Function in topology Relatively compact subspace – Subset of a topological...

be paracompact. The notion of paracompact space is also studied in pointless topology, where it is more well-behaved. For example, the product of any number...

mainstream geometry and topology, there are some systems that forgo it, e.g. noncommutative geometry and pointless topology. A "pointless" or "pointfree" space...

Complete Heyting algebras thus become a central object of study in pointless topology. Every Heyting algebra whose set of non-greatest elements has a greatest...

form the foundation of pointless topology, which, instead of building on point-set topology, recasts the ideas of general topology in categorical terms...

independence of choice from ZF, as well as providing the framework for pointless topology and Stone spaces. An active area of research is the univalent foundations...

stipulate a base set of points. For example, "pointless topology" (in other words, point-free topology, or locale theory) starts with a single base set...

Marshall Stone. Stone-type dualities also provide the foundation for pointless topology and are exploited in theoretical computer science for the study of...

memory access Locale (mathematics), a complete Heyting algebra used in pointless topology Locale (geographic), a geographic place where there is or was human...

sheaf theory, with geometric origins, and leads to ideas such as pointless topology. Categorical logic is now a well-defined field based on type theory...

entirely constructively. It also produced a more accessible spin-off in pointless topology, where the locale concept isolates some insights found by treating...

topology. Beyond these relations, topology can be looked at solely in terms of the open set lattices, which leads to the study of pointless topology....

between finite partial orders and finite distributive lattices. In pointless topology the category of spatial locales is known to be equivalent to the dual...

theory Picard–Vessiot theory Plane geometry Point-set topology see general topology Pointless topology Poisson geometry Polyhedral combinatorics a branch...

algebra Relatively complemented lattice Complete Heyting algebra Pointless topology MV-algebra Ockham algebras: Stone algebra De Morgan algebra Kleene...

subsets of X to determine X up to homeomorphism, which is relevant to pointless topology. Sobriety makes the specialization preorder a directed complete partial...

Hughes "Pointless", a series 7 episode of the British sitcom Not Going Out (which features the game show) Pointless topology, an approach to topology that...

theory) Listing number Mereotopology Noncommutative topology Pointless topology Set-theoretic topology Topological combinatorics Topological data analysis...

algebra. Locales are also called frames and appear in Stone duality and pointless topology. Locally finite poset. A partially ordered set P is locally finite...

Descent (category theory) Grothendieck topology Introduction to topos theory Subobject classifier Pointless topology Heyting algebra History of category...

partial lattices: not every pair of elements has a meet or join. Pointless topology Lattice of subgroups Spectral space Invariant subspace Closure operator...

discussed in Casati and Varzi (1999: ch. 5). Mereology Pointless topology Point-set topology Topology Topological space (with links to T0 through T6) Whitehead's...

spaces is an active area in set-theoretic topology. The analogue of Tychonoff's theorem in pointless topology does not require any form of the axiom of...

locales or complete Heyting algebras. They arise in connection with pointless topology and Stone duality. This distributive law is not equivalent to its...

famous duality of sober spaces and spatial locales, exploited in pointless topology. Every partially ordered set can be viewed as a category (where the...

mathematician working in topology and functional analysis. Her doctoral thesis was one of the initial sources of pointless topology. She has also been active...

Weibel; History of homological algebra Peter Johnstone; The point of pointless topology Stasheff, Jim (January 21, 1996). "The Pre-History Of Operads". In...