Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Such that any two distinct points are topologically distinguishable, i.e., there is an open set containing one of the points which does not contain the other point.
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

The theory is known as the KolmogorovArnoldMoser, or KAM, theory.

Now, there is such a quantity called Kolmogorov Complexity that concerns the maximum compressibility of bit strings, but that is not what you are talking about.
More creationist misconceptions about the eye  The Panda's Thumb

The Berry paradox has been related to the incompleteness phenomena also because of work (going back to the sixties and the seventies) in the socalled Kolmogorov complexity and algorithmic information theory.

A computer science idea more applicable to climate prediction is the notion of Kolmogorov complexity wherein you ask “What is the size of the smallest computer program able to generate the answer to some given problem?”

(This concept was later rediscovered by the Russian mathematician Kolmogorov, and is commonly called Kolmogorov complexity today.

Putting theory into practice  in this case, taking a theoretical construct such as Kolmogorov complexity, and applying it to physics  is not always trivial.
Jonathan Wells: Another ID Creationist Who Doesn't Understand Information Theory  The Panda's Thumb

Kolmogorov had been working on a problem related to the motion of particles and other objects.

In 1954, Kolmogorov provided a theoretical breakthrough that suggested it would be possible to predict the stability of such a system.

In Signature in the Cell, Meyer talks about three different kinds of information: Shannon information, Kolmogorov information, and a third kind that has been invented by ID creationists and has no coherent definition.
Stephen Meyer's Bogus Information Theory  The Panda's Thumb

All five questions are based on the Kolmogorov interpretation of information theory.
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