Dictionary
Acronyms and Abbreviations
A
ab: abelian
abs: absolute (value)
AC: axiom of choice
ACC: ascending chain condition
a.e.: almost everywhere
alg.: algebra
arg: argument of
a.s.: almost surely
asym: asymmetric, asymmetric
asso: associative
aut: automorphism
B
bd: boundary
BVP: boundary value proble
BWOC: by way of contradiction
C
calc: calculus, calculation
can: canonical (map)
card: cardinality, cardinal
cat.:category
CBS ineq.: Cauchy-Bunyakovsky-Schwartz inequality
cd: commutative diagram
CGWH: compactly generated weak Hausdorff
CH: continuum hypothesis
cl: closure
clsd: closed
cncv: concave
cntd: connected
cnvx: convex
codom, cod: codomain
coker, cok: cokernel
comm.: commutative
const: constant
conti.: continuous
Cor: corollary
cpt: compact
cpx,cx: complex
D
DC: axiom of dependent choice
DCC: decending chain condition
def: define, definition
dim: dimension
E
end: endomorphism
epi: epimorphism
eqn: equation
equiv.: equivalence, equivalent
ETS: enough to show
evec: eigenvector
eval: eigenvalue
F
f.d.: finite dimentional
fib: fibration, fiber
fin.: finite
FOL: first-order logic, first-order language
FT: Fourier transformation
FTC: fundamental theorem of calculus
func, fcn: function
G
gen’d: generated
glb: greatest lower bound
g.l.b.p.: greatest-lower-bound property
grp, gp: group
H
HEP: homotopy extension property
hom: homomorphism, homomorphic
homeo: homeomorphism, homeomorphic
hol: holomorphic (function)
I
id: identity
iff: if and only if
IH: induction hypothesis
im: image
Im: imaginary part
inc: inclusion map
inf: infimum
inj: injective
int: interior
inv: inverse, invariant
isom: isomorphism
IVP: initial value problem
L
LCH: locally compact Hausdorff
lem: lemma
LES, l.e.s.: long exact sequence
LHS: left-hand side
lim: limit
lin.: linear
lo: linear order
loset: linearly ordered set
lub.: least upper bound
l.u.b.p.: least-upper-bound property
M
max: maximum
mero: meromorphic (function)
mfd: manifold
min: minimum
MK: Morse-Kelley set theory
mod: modulo, modulus
mon: monoid
mono: monomorphism
MONS: maximal orthonormal system
mor: morphism
m-sble: measurable
N
nat. : natural
NGB: von Neumann-Bernays-Gödel set theory
NTS: need to show
n.v.s.: normed vector space
O
ode: ordinary differential equations
ONB: orthonormal basis
op.: operation, operator
ord: order, ordinal
P
pde: partial differential equatnions
pdf: probability distribution function
perm: permutation
pf: proof
po: partial order
poly.: polynomial
poset: partially ordered set
pr.: probability
prod.: product
prop: property
Q
QED: quantum eletrodynamics
Q.E.D.: (Quod erat demonstrandum) which was to be demonstrated
QFT: quantum field theory, quantum Fourier transformation
quant, q: quantum
QM: quantum mechanics
QT: quantum theory
R
ran: range
Re: real part
rel.: relation
resp.: respectively
RHS: right-hand side
rk: rank
rmk: remarks
RTP: required to prove
RTS: remain to show
S
seq.: sequence
SES, s.e.s.: short exact sequence
s.t.: such that, so that, subject to
sol: solution
sp.:space
spec: spectrum
spx, sx: simplex
sup: supremum
surj: surjective, surjection
symm, sym: symmetric, symmetry
T
TFAE: the following are equivalent
thm: theorem
top.: topology
tr.: trace, transformation
trans: transitive
U
univ.: universal
V
v.s.: vector space
W
wff: well-formed formula
WLOG: without loss of generality
WMA: we may assume
w.r.t.: with respect to, with regard to
WTP: want to prove
WTS: want to show, wish to show
Z
ZF: Zermelo-Fraenkel set theory
ZFC: Zermelo-Fraenkel set theory with the axiom of choice