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Mengers

Mengers is a surname most prominently associated with Karl Menger (1902–1985), an Austrian-born American mathematician who made foundational contributions to topology, geometry, and combinatorics. Through his work, several mathematical concepts bear the name Menger.

Menger's theorem in graph theory states that for any two nonadjacent vertices in a finite graph, the

The Menger sponge is a three-dimensional fractal constructed by iteratively removing the central cube and the

The Menger curve, also known as the Menger universal curve, is a one-dimensional topological space that is

In summary, Mengers most commonly refers to the mathematical legacy of Karl Menger, including fundamental theorems

minimum
number
of
vertices
whose
removal
disconnects
them
equals
the
maximum
number
of
pairwise
internally
vertex-disjoint
paths
between
them.
A
variant
exists
for
edge-disjoint
paths.
centers
of
each
face
from
a
3x3x3
cube,
leaving
20
self-similar
pieces
at
each
stage.
The
Hausdorff
dimension
of
the
sponge
is
log(20)/log(3)
≈
2.7268,
and
it
serves
as
a
classic
example
of
a
fractal
with
non-integer
dimension
and
intriguing
topological
properties.
universal
for
all
1-dimensional
separable
metric
spaces,
reflecting
Menger’s
influence
in
geometric
topology.
and
fractal
constructs
that
bear
his
name.