# Questions tagged [definitions]

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### What is the standard definition of dual of disconnected planar graph when underlying graph derives 'product structure' over connected graphs?

Dual graph of a plane graph has a standard definition https://en.wikipedia.org/wiki/Dual_graph and an edgeless graph on $n$ vertices is planar. What is the standard dual graph of such a graph? Update ...
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### Coming up with a equivalent (or close) definition for an average which is easier to compute? [closed]

Continuing from my last question, I understand that my definition is unclear so I have modified it. Since no one has answered my question on math stack exchange, I decided to ask here. Definition ...
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### Reference Request: A definition of topology using monads (a.k.a. halos)

In nonstandard analysis, there is a way of studying topological spaces known as "monads" (more commonly known as halos, as it turns out). The monad of a point $x$ (written $\mu(x))$ is the set of all ...
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### How is the minimax oracle used to find the oracle complexity of projected subgradient?

I am going through a set of blog posts on the complexity of projected gradient method. https://blogs.princeton.edu/imabandit/2013/03/15/orf523-oracle-complexity-large-scale-optimization/ defines the ...
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### Main statement as theorem or corollary

In a text there will often be a few important results that are usually called Theorems. Intermediate statements are called Lemmas, and statements that follow immediately from previous results are ...
### Characterization of non-Zeno functions $f:\mathbb{R}\rightarrow \{0,1\}$
[Edit: I tried to integrate Nate's comments (see below).] In the context of automata over continuous time, consider Boolean-valued functions $f:\mathbb{R}\rightarrow \{0,1\}$. There are uncountably ...