Interior algebra

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Relationships to other areas of mathematics

Power set Complete Atomic Isomorphic Embedded

45 related topics

Stone duality and representation for interior algebras

Stone duality Boolean spaces Kripke Jónsson Tarski

11 related topics

Morphisms of interior algebras

Homomorphisms If and only if Morphisms Meets Joins

10 related topics

Overview

Abstract algebra Algebraic structure Interior Topology Modal logic

16 related topics

Topics to explore

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Overview

Abstract algebra
Algebraic structure
Interior Interior (topology)
Topology
Modal logic
Boolean algebras Boolean algebra (structure)
Set theory
Propositional logic
Variety Variety (universal algebra)
Modal algebras Modal algebra
Topologies Topological space
Universal algebra
Neighbourhoods Neighbourhood (mathematics)
Filter Filter (mathematics)
(meet)-semilattices Semilattice
Neighbourhood (semi)lattices Neighbourhood lattice?action=edit&redlink=1

Definition

Signature Signature (logic)
Unary operator
Dual Duality (order theory)
Closure operator
Wim Blok

Open and closed elements

Open Open set
Complements Complement (order theory)
Closed Closed set
Regular open Regular open set
Clopen Clopen set

Morphisms of interior algebras

Homomorphisms Homomorphism
If and only if
Morphisms Morphism
Meets Meet (order theory)
Joins Join (order theory)
Sikorski Roman Sikorski
Inverse image
Continuous map
Covariant Functor
Category theoretic

Relationships to other areas of mathematics

Power set
Complete Completeness (order theory)
Atomic Atomic (order theory)
Isomorphic Isomorphism
Embedded Embedding
Field of sets
Category of topological spaces
Category Category theory
Dually isomorphic Dual (category theory)
Open map
Empty Empty set
Indiscrete Indiscrete space
Simple Simple algebra
Discrete Discrete space
Almost discrete Almost discrete space?action=edit&redlink=1
Semisimple Semisimple algebraic group
Alexandrov topology
Connected Connected space
Directly indecomposable
Ultraconnected Ultraconnected space
Finitely subdirectly irreducible Finitely subdirectly irreducible?action=edit&redlink=1
Compact Compact space
Subdirectly irreducible
Theory Theory (logic)
Algebraic semantics Lindenbaum–Tarski algebra
Logically equivalent Logical equivalence
Logician Philosophical logic
C. I. Lewis Clarence Irving Lewis
Operators Unary operation
Binary relation

Stone duality and representation for interior algebras

Stone duality
Boolean spaces Boolean space
Kripke Saul Kripke
Jónsson Bjarni Jónsson
Tarski Alfred Tarski
Boolean algebras with operators Boolean algebras with operators?action=edit&redlink=1
Esakia duality
Stone's representation theorem Stone's representation theorem for Boolean algebras
Topological basis
Topological semantics Topological semantics?action=edit&redlink=1
McKinsey J.C.C. McKinsey

Metamathematics

First-order theory
Undecidable Decision problem
Hereditarily undecidable Hereditarily undecidable?action=edit&redlink=1
Chain Chain (order theory)

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Map overview Semantic statistics

Nodes104

Edges103

Triples126

Avg. degree1.98

Density0.019231

Components1

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Interior algebra

Top relations

related to References · 28

Interior algebra → Alfred Tarski, Algebra Universalis, Amsterdam, Annals, Applied Logic, Bezhanishvili, Blok, Cape Town Department, Closure, Esakia, Fundamenta Mathematicae, Heyting, Interior Algebras, Intuitionistic, Mathematics, McKinsey, Mines, Morandi, Naturman, On

related to Stone duality and representation for interior algebras · 24

Interior algebra → An, Boolean, Building, By, Esakia, Hansoul, Heyting, Homomorphisms, In, Jónsson, Kripke, Leo Esakia, Lewis's, McKinsey, Naturman, Pierce, S4-algebras, Stone, Stone's, Tang Tsao-Chen

related to Continuous morphisms · 10

Interior algebra → Boolean, In, Later, Naturman, On, Schmid, Sikorski, Sikorski's, The, This

related to Monadic Boolean algebras · 9

Interior algebra → Any, Boolean, In, Kripke, Moreover, S5, The, They, This

related to Preorders · 9

Interior algebra → Boolean, Given, In, Kripke, Preordered, S4, S4-frames, Since, The Kripke

related to Derivative algebras · 7

Interior algebra → Boolean, Derivative, From, Given, Hence, S4, Thus

related to Modal logic · 7

Interior algebra → Given, Lindenbaum, S4, Tarski, The, Then, This

related to Heyting algebras · 6

Interior algebra → Boolean, Every Heyting, Grz, Heyting, S4, The

related to Boolean homomorphisms · 5

Interior algebra → Applications, Boolean, Early, Such, The

related to Open and closed elements · 5

Interior algebra → An, Boolean, Elements, Interiors, The

Important terminology Word statistics

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Important terminology

interior algebras boolean algebra open closure topology topological closed elements sets modal operator form homomorphisms tarski called logic set duality

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Interior algebra	is a	certain type of algebraic structure that encodes the idea of the topological interior of a set	0.90	text
Interior algebra	is a	algebraic structure with the signature	0.90	text
Interior algebra	is a	intersection of the former two topologies	0.90	text
Interior algebra	related to Boolean homomorphisms	Early	0.60	section
Interior algebra	related to Boolean homomorphisms	Boolean	0.60	section
Interior algebra	related to Boolean homomorphisms	Such	0.60	section
Interior algebra	related to Boolean homomorphisms	The	0.60	section
Interior algebra	related to Boolean homomorphisms	Applications	0.60	section
Interior algebra	related to Continuous morphisms	The	0.60	section
Interior algebra	related to Continuous morphisms	Sikorski's	0.60	section
Interior algebra	related to Continuous morphisms	This	0.60	section
Interior algebra	related to Continuous morphisms	Boolean	0.60	section

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Relationships to other areas of mathematics

Stone duality and representation for interior algebras

Morphisms of interior algebras

Overview

Key facts & relationships

Topics to explore

Overview

Definition

Open and closed elements

Morphisms of interior algebras

Relationships to other areas of mathematics

Stone duality and representation for interior algebras

Metamathematics

Advanced semantic analysis

Map overview Semantic statistics

Interior algebra

How this topic connects Entity context

Interior algebra

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges