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A Compact Set that is not Closed
A Nonempty Set is Compact in the Order Topology iff it is Tightly Bounded and Complete
A Simple Function Induces a Finite Sigma Algebra
A Topological Basis can be thinned out by a smaller one
A Vector Space is Finite-Dimensional iff it has a Finite Spanning Set
A Vector Space is Infinite-Dimensional iff its Linearly Independent Set Size is Unbounded
All Simple Functions can be Written in Standard Form
Bounded Continuous Function Space
Closed Subset of a Compact Set is Compact
Compact
Compact Function Space
Compact Sets are Separable from Points in a Hausdorff Space
Compact Spaces are Complete
Continuous Functions Preserve Compactness
Dimension of a Vector Space
Dimension of a Vector Space lower bounds Spanning Set size
Dimension of a Vector Space upper bounds Linearly Independent Set sizee
Discrete Topology
Equivalent Conditions for Local Compactness of Hausdorff Spaces
Finite-Dimensional Vector Space
Finite Equation System
Formula
Formulas are Finite
Graph Deficiency
Indiscrete Topology
Infinite Pigeonhole
Liminf of Set Sequence
Linearly Dependent
Linearly Independent Set Size is Unbounded iff there exists an Infinite Linearly Independent Set
Martingale Convergence Theorem
Product of Topological Manifolds is a Manifold
Restricting an Extended Norm to elements of Finite Norm form a Normed Vector Space
Satisfaction Relation
Simple Function
Superset of Linearly Dependent Set is Linearly Dependent
Term
Terms are Finite
The Empty Set is Linearly Independent
The Induced Sigma Algebra of a Borel Function is Finite iff it is Simple
The Term Set is the Union of Term Sets of all Complexities
Topological Space
Topology Generated by a Basis
Total Subset
Univariate Monomials form Infinite Basis for Univariate Polynomials on Complex Numbers
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