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Everything about Closure operator
Mathematical operator
In mathematics, a closure operator on a set S is a function from the power set of S to itself that satisfies the following conditions for all sets Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Closure operatorA 5-minute orientation
- Skim a recent paper: A multifidelity deep operator network approach to closure for multiscale systemsInfluential work since 2022
- Pick up a classic book: Military base closuresThe most-reprinted book on the subject
- Read the landmark paper: Fuzzy topology: Fuzzy closure operator, fuzzy compactness and fuzzy connectednessCited 75 times
- Go sideways: Alexandrov topologyA closely related topic
- Go sideways: Axiomatic foundations of topological spacesA closely related topic
📖 Definitions
Noun A function which maps any subset X of S onto another such subset (or possibly X itself) called the closure of X (thus providing a mathematical means to define closure).
🏆 Landmark papers (most cited)
Fuzzy topology: Fuzzy closure operator, fuzzy compactness and fuzzy connectedness
Graded consequence relations and fuzzy closure operator
On the closure of the numerical range of an operator
Weyl Closure of a Linear Differential Operator
Fuzzy θ‐closure operator on fuzzy topological spaces
Equational closure operator and forbidden semidistributive lattices
Neighborhoods with respect to a categorical closure operator
Connectedness with Respect to a Closure Operator
🆕 Influential since 2022
A multifidelity deep operator network approach to closure for multiscale systems
Data-driven stochastic closure modeling via conditional diffusion model and neural operator
Closure of the Laplace-Beltrami Operator on 2D Almost-Riemannian Manifolds and Semi-Fredholm Properties of Differential Operators on Lie Manifolds
A closure operator respecting the modular j-function
Closure Ordinal of Immediate Derivability Operator of Infinitary Action Logic
📚 Books worth reading
- 📕Military base closuresUnited States. General Accounting Office · 1992
Categorical Closure OperatorsGabriele Castellini · 2003- 📕Hearing on National Defense Authorization Act for fiscal year 2008 and oversight of previously authorized programs before the Committee on Armed Services, House of Representatives, One Hundred Tenth Congress, first sessionUnited States. Congress. House. Committee on Armed Services. Readiness Subcommittee. · 2008
- 📕Hearing on National Defense Authorization Act for Fiscal Year 2009 and oversight of previously authorized programs before the Committee on Armed Services, House of Representatives, One Hundred Tenth Congress, second sessionUnited States. Congress. House. Committee on Armed Services. Readiness Subcommittee. · 2009
- 📕Hearing on National Defense Authorization Act for Fiscal Year 2010 and oversight of previously authorized programs before the Committee on Armed Services, House of Representatives, One Hundred Eleventh Congress, first sessionUnited States. Congress. House. Committee on Armed Services. Readiness Subcommittee · 2010
- 📕Hearing on National Defense Authorization Act for Fiscal Year 2013 and oversight of previously authorized programs before the Committee on Armed Services, House of Representatives, One Hundred Twelfth Congress, second sessionUnited States. Congress. House. Committee on Armed Services · 2012
- 📕Sulla caratterizzazione dei reticoli di operatori di chiusura su un reticolo completoMaria Pierina Manara · 1968
Categorical structure of closure operators with applications to topology, algebra, and discrete mathematicsDikran N. Dikranjan · 1995
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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