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1. 2-Dimensional rotation matrix
2. A-(A-B) = A cap B
3. ASN
4. A cap (B-C) = (A cap B) - C
5. A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections
6. A compact and convex subset of Euclidean n-space with non-empty interior is a closed n-cell and its interior is an open n-cell
7. A compact and convex subset of Euclidean n-space with non-empty interior is a closed n-cell and its interior is an open n-cell/Statement
8. A continuous map induces a homomorphism on fundamental groups
9. 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)
10. A function is continuous if and only if the pre-image of every basis element is open
11. A linear map is injective if and only if its kernel is trivial
12. A linear map is injective if and only if the image of every non-zero vector is a non-zero vector
13. A linear map is injective if and only if the kernel contains only the zero vector
14. 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
15. 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
16. A map is continuous if and only if the pre-image of every closed set is closed
17. A monotonically increasing sequence bounded above converges
18. A pair of identical elements is a singleton
19. A pre-measure on a semi-ring may be extended uniquely to a pre-measure on a ring
20. A proper vector subspace of a topological vector space has no interior
21. A sequence consisting of the nth terms of the sequences in a Cauchy sequence of elements in any little-L space is itself a Cauchy sequence of complex numbers
22. A set is bounded if and only if for all points in the space there is a positive real such that the distance from that point to any point in the set is less than the positive real
23. A set is dense if and only if every non-empty open subset contains a point of it
24. A set is open if and only if every point in the set has an open neighbourhood contained within the set
25. 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
26. 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
27. A subset of a topological space is open if and only if it is a neighbourhood to all of its points
28. A subspace of a Hausdorff space is Hausdorff
29. A topological space is connected if and only if the only sets that are both open and closed in the space are the entire space itself and the emptyset
30. A topological space is disconnected if and only if it is homeomorphic to a disjoint union of two or more non-empty topological spaces
31. A topological space is disconnected if and only if there exists a non-constant continuous function from the space to the discrete space on two elements
32. Abelian group
33. Absolute value
34. Absolute value (object)
35. Abstract Algebra
36. Abstract Algebra (subject)
37. Abstract simplicial complex
38. Addition of vector spaces
39. Additive function
40. Adjunction
41. Adjunction topology
42. Alec's base 5 conventions
43. Alec's c.d.f-sidestepping sampling method
44. Alec's expected value trick
45. Alec's ordered data test
46. Alec's puzzles
47. Alec's puzzles/Statistics
48. Alec's remaining probability bound
49. Alec's sample mean bound
50. Alec's taxonomy of units

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