What are the most overloaded words in mathematics? This is community wiki.  In each answer, please list one word at the top and below that list as many different meanings of that word in mathematics as you can think of, preferably with links or definitions.  ("Adjective" and "adjective noun" count as the same adjective.)  People should edit previous answers as appropriate.
(This is mostly just for fun, but I'm also curious if there have been successful attempts to rename concepts that involve overused words.)
Edit:  I may have been slightly unclear about the intent of this question.


*

*When I say "overused" I don't mean "used too often," I mean "used in too many different ways."  So I'll change the title of the question to reflect this.

*Different concepts named after the same mathematician, while potentially confusing, are understandable.  

*I mostly had in mind adjectives that get recycled in different disciplines of mathematics.  Different uses of the same noun tend to be less confusing, e.g. the example of "space" below.  I think it's good to be intentionally vague about what we consider a "space."

 A: Complete/Completion
complete metric spaces,
complete measure spaces,
completing a ring at an ideal,
complete graph
complete category
complete lattice
and many more uses (a lot in computation theory/logic) at
http://en.wikipedia.org/wiki/Completeness
A: Regular.  To start off:
The regular representation of a group $G$ over a field $k$ is the action on $k[G]$ given by group multiplication.
A topology is regular if a closed set and a point not in that set can be separated by disjoint open sets.
A point $\zeta_0$ on the boundary of a domain in $\mathbb C$ is called regular if there exists a subharmonic barrier function $b(z)$ defined within $D$ near $\zeta$. This may not be the standard definition but Gamelin's complex Analysis defines it as a subharmonic function $\omega(z)$ on $\{|z-\zeta_0|<\delta\}\cap D$ which is negative everywhere, tends to 0 at $\zeta_0$, but $\limsup(\omega(z))<0$ as $z$ tends to any other boundary point of $D$ within distance $\delta$ of $\zeta_0$.
I've borrowed/paraphrased the following from the Wikipedia disambiguation page but removed a couple that either are not too relevant to pure math or qualify the "regularity" more.  Feel free to put them in too.
Regular cardinal, a cardinal number that is equal to its cofinality
Regular category
Regular element, and regular sequence and regular immersion.
Regular code, an algebraic code with a uniform distribution of distances between codewords
Regular graph, a graph such that all the degrees of the vertices are equal
The regularity lemma, which has nothing to do with regular graphs
Regular polygon, and regular polyhedron
Regular prime: a prime $p$ that does not divide the class number of the $p$th cyclotomic field $\mathbb Q[\zeta_p]$.
Regular surface in algebraic geometry
Regularity of an elliptic operator
JS Milne's comment: A regular map is a morphism of algebraic varieties.
Regular value of a differentiable map
Regular ring (Note: this definition can be made noncommutative. A right noetherian ring R is said to be right regular if every finitely generated right R-module has finite global dimension.  See Lam's Lectures in Modules and Rings, Section 5G.)
(von Neumann) Regular ring
Regular language, a language that can be accepted by a finite state machine.
Absolutely regular is a synonym for $\beta$-mixing in stochastic processes.
Regular matroid, a matroid which is representable over every field.  In this sense, all graphs are regular (their cycle matroids are regular), which has nothing to do with regular graphs.    
A: Uniform. Most of these do have the intuitive sense of "being locally the same everywhere," but by no means all of them, and their sheer number gets pretty confusing.

*

*uniform polytope

*uniform convergence in machine learning (related but not the same)

*uniform distribution

*uniform convergence

*uniform continuity

*uniform integrability

*uniform boundedness

*uniform equicontinuity

*uniform space (from uniform continuity)

*The Riemann uniformization theorem

*uniform circuit family (complexity theory)

*Gowers uniformity norms

*uniform modules

*uniform matroid
A: Normal


*

*Normal distribution

*Normal vector

*Normal space

*Normal extension

*Normal subgroup

*Normal operator

*Normal convergence
A: "Let" (which does not meet the 15 character minimum)
A: Spectrum.
From http://en.wikipedia.org/wiki/Spectrum#Mathematics:
Spectrum (homotopy theory)
Spectrum of a matrix, in linear algebra
Spectrum of an operator, in functional analysis (a generalisation of the spectrum of a matrix)
Spectrum of a ring, in commutative algebra
Spectrum of a C*-algebra
Spectrum of a theory, in mathematical logic
Stone space of Boolean algebra
A: The most overloaded word in mathematics is the empty word. The one that comes between $a$ and $b$ in $ab$, meaning multiplication. Or does it mean the binary operator in a more general monoid or group? Or one of the two binary operators in a ring? Or the action of a monoid or group on a set, or the action of the base ring on a module? (And if so, is it a left or right action?) Or the application of a function (or functor) on its argument? Or even three or four of these in one expression, or, even worse, two at the same time in the very same place, exploiting associativity to ensure the ambiguity is mostly harmless? Or one of countless other things?
A: Closed:
Closed set
Closed surface
Closed geodesic
Closed function
This question is closed :-)
A: Perfect


*

*A perfect integer is the sum of its proper divisors.

*A perfect complex is locally quasi-isomorphic to a bounded complex of finitely generated projective modules.

*A perfect field is a field whose algebraic extensions are all separable.

*A perfect square is a natural number of the form $n^2$ for some $n \in \mathbb{N}$.

*A perfect group is equal to its own commutator subgroup.

*A perfect set is a closed set with no isolated points.

*A perfect graph is a graph such that each induced subgraph's chromatic number is equal to its clique number.  

A: Abelian.

*

*Abelian Group (also other commutative algebraic structures, and related structures like Abelian extensions)

*Abelian theorem

*Abelian Variety (as well as surface)

*Abelian function

*Abelian integral

*Abelian Category

*Abelian equation (used in web geometry, also appears as Abelian relation)

A: Base/Basis


*

*Group Base

*Topological Base/Basis

*Algebra Basis

*Vector Space Basis

*Logarithm Base
Edit: It's been clarified that we're really more interested in adjectives but I think the use of base in these examples are quite substantially different.
A: Reflexive (relation, locally convex (Banach) space, operator algebra, module, a.s.o.)
It is an adjective.
Proposition Every infinite dimensional von Neumann algebra is reflexive, and also
it is not reflexive.
A: Canonical... would be a canonical example.  I guess.
A: Simple


*

*Simple field extension

*Simple group

*Simple ring

*Simple module

*Simple algebra

*Simple graph

*Simple polygon

*Simple curve

*Simple zero

*Simple function

*Simple connectivity

*Simple root

A: If you happen to work on del Pezzo surfaces, don't make the mistake of standing in an airport security line talking about "blowing up a plane at eight points".
(Yes, this really happened, and ended happily, or at least not in Guantanamo.)
A: "Cauchy theorem"
A: Obvious
"'Obvious' is the most dangerous word in mathematics." -- E. T. Bell  
Example: all examples You are using to answer this post are obvious.
A: Index, Order, and Rank certainly qualify
A: Hedgehog.
Just one use of this word in mathematics is "overuse".
A: Natural
Very often I read things like "Now, it is natural to ask...", ""X is a natural generalization of Y" or "A natural question is..." when the problems are by no means natural, and the feeling of "naturalness" is only achieved post factum. 
A: Separable


*

*Separation axioms ($T_0$,$T_1$, etc.)

*Separable space (countable dense subset)

*Separable differential equation

*Separable scheme (although analogous at least in spirit to the Hausdorff axiom)

*Separable field extensions / polynomials

*Separable subgroup (ie a subgroup that's closed in the profinite topology)

*Separable quantum state (it means mixed unentangled)

A: Admissible, a colorless synonym for "which lies in the class of objects we're studying".
A: Primitive.


*

*Primitive polynomial (in the sense of finite field theory, namely minimal polynomial of field generator)

*Primitive polynomial (in the sense of ring theory, namely gcd of coefficients is 1)

*Primitive element (and primitive extension)

*Primitive function (antiderivative)

*Primitive permutation group (no non-trivial equivalence relation preserved)

*Primitive polytope (rarely used, I think).

*(left) Primitive ring

*Primitive recursion (in logic and complexity theory)

*Primitive (nonnegative) matrix
A: trivial
Besides being a synonym to 'obvious', like in 'the proof is trivial', it has the meaning of 'shallow' ('the question is trivial') and moreover denotes a bunch of mathematical notions:
trivial group
trivial representation
trivial topology
trivial solution (in ODE/PDE)
etc.
Sometimes it produces confusion as it is not quite clear which sort of triviality is meant.
A: Elliptic.


*

*Elliptic Integral

*Elliptic Equation

*Elliptic Operator

*Elliptic Curve

*Elliptic(al?) Point

*Elliptic Function

*Elliptic (Moebius) Transformation
Of course, these are not entirely independent, but there are several distinct meanings involved.
A: Deep
I'm not sure whether it has one meaning or zero.  Either way, I think that it is deeply overused.
A: Nice
Mostly because it is such a local word - 'such and such is called 'nice' if...'
Segal once formally defined a 'nice simplicial space' - these days called simplicial spaces satisfying the Segal condition, a very sensible move.
A: The word "stable" is used in many different contexts. Also "elementary" has many usages. The word "lattice" has two entirely different meanings which are ar time confusing. So is the word "field".
I have two more: "deterministic" refers sometimes as  "not random" and it is also a central concept in computational complexity where "non deterministic" has another meaning (very different from random). The word "classical" is used in various confusing ways.
A: Generically
A word used a lot when you don't want to precisely specify under which conditions something is true, but its true in most cases. An example would be that generically all square matrices are invertible.
The precise meaning of this - at least in algebraic geometry - is that whatever property we are talking about is true on a dense open subset. Another example would be given a function between two smooth manifolds then a generic point in the target manifold is not a critical value of the function.
A: Well-defined.  Overused not because it has too many definitions but because it has too few.
A: Space
Affine space
Banach space
Cauchy space
Euclidean space
Function space
Hardy space
Hilbert space
Inner product space
Kolmogorov space
Krein space
Klein space
Pontrjagin space
Lp space
Measure space
Metric space
Minkowski space
Normed vector space
Locally convex space
Linear topological space 
F-space
Frechet space
Nuclear space
Operator space
Affine space
Projective space
Polish space
Quotient space
Sobolev space
Topological space
Uniform space
Vector space
Harmonic spaces 
Conformal space 
Complex analytic space
Affinely connected space
Algebraic space
Symplectic space
Measurable space
Measure space
Probability space
Riemann space
Lorentzian space
And so on.
A: -ary
-ary, as in $k$-ary numeral $s$, refers to the number $k$ of values in the domain $K = \lbrace 0, 1, \ldots, k-1 \rbrace$ that affords the basis of numeration.
-ary, as in $k$-ary relation $L$, refers to the number of domains $X_1, \ldots, X_k$ for which $L \subseteq X_1 \times \ldots \times X_k$.
-ary, as in $k$-ary operation $f$, refers to the number of domains in the domain of the function $f : X_1 \times \ldots \times X_k \to Y$, the rubric being, "a $k$-ary operation is a $(k+1)$-ary relation".
Some writers use Greek roots and the Greek suffix "-adic" for the number of domains in a relation, hence medadic, monadic, dyadic, triadic for relations of 0, 1, 2, 3 places, respectively.  This usage actually has a degree of historical precedence and it can serve to sidestep conflicts with the domainance of binary numerals in our modern world, but of course the wrinkle but moves to other domains where writers are adicted to other habits.
NB. All puns are intended.
A: Elementary
Sense 1 = basic, simple, concerning the elements ("first steps") of a subject.


*

*elementary fact

*elementary introduction

*elementary problem

*elementary proof


Sense 2 = treating mathematical objects as elements of a collection.


*

*elementary number theory

