Difference between revisions of "Category:Todo"

A

• ► All Notes‎ (1 C, 22 P)

D

• ► Dire pages‎ (18 P)

F

• ► Function Terminology‎ (7 P)

N

• ► Notes‎ (7 C, 22 P)

P

• ► Pages requiring cleanup‎ (1 C, 3 P)
• ► Pages requiring exploration‎ (1 C, 2 P)
• ► Pages requiring proof‎ (1 C)

P cont.

• ► Pages requiring proof writeup‎ (3 P)
• ► Pages requiring proofs‎ (10 C, 128 P)
• ► Pages requiring references‎ (7 C, 83 P)
• ► Pages requiring work‎ (3 C, 36 P)
• ► Provisional pages‎ (3 C, 19 P)

S

• ► Set operations‎ (5 P)
• ► Site project tasks‎ (2 P)

S cont.

• ► Stub pages‎ (13 C, 386 P)

T

• ► Todo: Navbox project‎ (10 P)
• ► Todo: Subject page refactoring‎ (1 P)
• ► Types of morphism‎ (3 P)
• ► Types of relation‎ (3 P)

X

• ► XXX Todo‎ (1 C, 96 P)

A

• A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections
• A function is a measure iff it measures the empty set as 0, disjoint sets add, and it is continuous from below (with equiv. conditions)
• A map from two sigma-algebras, A and B, is measurable if and only if for some generator of B (call it G) we have the inverse image of S is in A for every S in G
• A map is continuous if and only if each point in the domain has an open neighbourhood for which the restriction of the map is continuous on
• A map is continuous if and only if the pre-image of every closed set is closed
• A subset of a topological space is disconnected if and only if it can be covered by two non-empty-in-the-subset and disjoint-in-the-subset sets that are open in the space itself
• A subset of a topological space is disconnected if and only if it can be covered by two non-empty-in-the-subset and disjoint-in-the-subset sets that are open in the space itself/Statement
• Template:Abstract algebra navbox
• Additive function
• Alec's taxonomy of units
• Algebra (linear algebra)
• Books:Algebra I: Rings, modules and categories - Carl Faith
• Algebra of sets
• Almost always
• Arc length

B

• Notes:Bash
• Basis for a topology
• Notes:Basis for a topology/McCarty
• Bilinear form
• Borel sigma-algebra
• Borel sigma-algebra generated by
• Borel sigma-algebra generated by/Claim 1
• Bounded set
• Box topology

C

• Canonical projections of the product topology
• Cardinality
• Cartesian product
• Categorical isomorphism
• Category
• Cauchy criterion for convergence
• Cauchy sequence
• Cauchy-Schwarz inequality
• Characteristic property of the direct product module
• Characteristic property of the direct product module/Statement
• Characteristic property of the direct product module/Statement/Diagram
• Characteristic property of the direct sum module
• Characteristic property of the direct sum module/Statement
• Characteristic property of the direct sum module/Statement/Picture
• Characteristic property of the disjoint union topology
• Characteristic property of the disjoint union topology/Statement
• Characteristic property of the product topology
• Characteristic property of the product topology/Statement
• Characteristic property of the product topology/Statement/Diagram
• Characteristic property of the subspace topology
• Class of sets closed under complements properties
• Classes of continuously differentiable functions
• Closed set
• Closed set in a compact space is compact
• Common data type ranges
• Commutator subgroup
• Compact set in a Hausdorff space is closed
• Compact subspace of a Hausdorff space is closed
• Compactness
• Compactness/Uniting covers proof
• Complement
• Complex conjugate
• Composition of measurable maps is measurable
• Conditions for a generated Dynkin system to be a sigma-algebra
• Conjugation
• Connected (topology)
• Connected (topology)/Equivalent conditions
• Continuity and non-surjective functions
• Notes:Continuous at a point
• Continuous map
• Talk:Continuous map
• Contravariant functor
• Convergence of a sequence

C cont.

• Covariant functor
• Covering space
• Cyclic subgroup

D

• De Morgan's laws
• Deformation retraction
• Deformation retraction/Definition
• Derivative
• Derivative (analysis)
• Notes:Diff algorithm
• Differentiability
• Doctrine:Differentiation notation & terminology
• Direct product module
• Direct sum (ring)
• Discrete metric and topology
• Disjoint
• Disjoint union (set)
• Disjoint union topology
• Notes:Dual basis
• Dual vector space
• Dynkin system
• Dynkin system generated by
• Dynkin system/Proof that definitions 1 and 2 are equivalent

E

• Editing guide
• Equivalence class
• Equivalence relation induced by a function
• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere
• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/1 implies 2
• Equivalent statements to a set being dense
• Equivalent statements to compactness of a metric space
• Euclidean algorithm
• Euclidean metric
• Euclidean norm
• Every convergent sequence is Cauchy
• Every injection yields a bijection onto its image
• Every lingering sequence has a convergent subsequence
• Every lingering sequence has a convergent subsequence/Proof
• Every sequence in a compact space is a lingering sequence
• Every sequence in a compact space is a lingering sequence/Proof
• Example comparing bilinear to linear maps
• Exists functor
• Expected value
• Extending pre-measures to measures
• Extension
• External direct sum
• External direct sum module

F

• Factoring a function through the projection of an equivalence relation induced by that function yields an injection
• Field
• First order language
• Formula (FOL)
• Function terminology
• Functional Analysis (subject)
• Functor

G

• Generated subgroup
• Geometric independence
• Given a topological manifold of dimension 2 or more and points p1, p2 and q where q is neither p1 nor p2 then a path from p1 to p2 is path-homotopic to a path that doesn't go through q
• Greater than or equal to
• Greater than or equal to/Epsilon form
• Notes:Grid iteration
• Group
• Notes:Group isomorphism theorems

H

• Herbrand domain
• Notes:Hereditary sigma-ring
• Hereditary sigma-ring
• Homeomorphism
• Homotopic maps
• Homotopy class

I

• If a subsequence of a Cauchy sequence converges then the Cauchy sequence itself also converges

I cont.

• Index of notation
• Index of notation/P
• Inner product
• Template:Inner product and Hilbert spaces navbox
• Inner product examples
• Integral of a positive function (measure theory)/Definition
• Integration by substitution
• Interior
• Lesson:Introduction to computing machines
• Invariant of an equivalence relation
• Isometry

L

• Lebesgue number lemma
• Limit
• Limit of increasing sequence of sets
• Limit point
• Linear independence
• Site:List of pages that need to be referenced by obvious pages
• Lower bound

M

• Maps
• Matrix
• Mdm of the Poisson distribution
• Measurable map
• Measure
• Measure Theory
• Doctrine:Measure theory terminology
• Measure/Infobox
• Measures are monotonic and subtractive
• Metric
• Metric space
• Template:Metric spaces navbox
• Metric subspace
• Min/max
• Module homomorphism
• Notes:Modules
• Monomial
• Monotonic
• Morphism
• Motivation for smooth manifolds
• Motivation for tangent space
• Motivation for tangent space definitions

N

• Neighbourhood
• Norm
• Normal subgroup
• Normal topological space
• Notation

O

• Open and closed maps
• Open ball
• Open set
• Ordering
• Overview of partial orders

P

• Parametrisation
• Passing to the quotient (function)
• Poisson race distribution
• Positive and negative parts of a function
• Pre-image sigma-algebra
• Talk:Pre-image sigma-algebra
• Pre-measure
• Pre-measure/Properties in common with measure
• Printf family
• Probability space
• Template:ProbMacro
• Product topology
• Projection
• Projector
• Properties of classes of sets closed under set-subtraction
• LibSR:Prototype