Tagged Questions
5
votes
1answer
81 views
Is the variant direct image mathematically significant?
Preimages have the property that for an arbitrary function $f : X \rightarrow Y$ and all $B \subseteq Y$ it holds that $$f^{-1}(B^c)=[f^{-1}(B)]^c.$$
However, the analogous statement for direct ...
2
votes
3answers
93 views
Should I put interpunction after formulas?
I am presently doing my first substantial piece of mathematical writing, hence this, probably somewhat silly, question.
How does display-style mathematics interact with punctuation?
More ...
1
vote
0answers
33 views
Is there a common notation for the labelled degree of a vertex?
Let $G$ be an undirected graph with labelled edges. The labelled degree of a vertex $v \in V(G)$ is the number of edges incident to $v$ with distinct labels.
The definition of the labelled degree ...
6
votes
1answer
243 views
What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?
Sometimes reading on wikipedia or in this site (and in very different context like topology, arithmetic and logic) I have found these symbols $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$. They are ...
6
votes
1answer
216 views
Is there a rigorous theory of context, whereby sets can gain additional structure within a context?
Consider sets $G$ and $H$ and a function $f : G \rightarrow H$. So far, it doesn't really make sense to ask whether $G$ and $H$ are groups (technically, the answer is "no, they're not groups"), and ...
2
votes
1answer
77 views
Diagrammatic (Postfix) Composition of Functions
Consider the functions $f : X \to Y$ and $g : Y \to Z$. According to the Wikipedia articles on Function Composition, the application of $f$ to an input $x$ can be written as $xf$ (as opposed to the ...
2
votes
2answers
54 views
Why is $S/R$ a ring extension?
If $S$ is a ring and $R \subset S$ is a subring it's common to write that $S/R$ is an extension of rings. I frequently find myself writing this and read it quite often in textbooks and lecture notes. ...
1
vote
0answers
27 views
Enumeration of symbols in grammatical expressions or vertices in tree graphs
I have expressions (type of a function) like e.g.
$$f:(A\to B)\to C \to (D\to E)\to F.$$
(Where I understand $A\to B\to C$ as $A\to (B\to C)$, in case that is relevant.)
There might be information ...
3
votes
2answers
130 views
Generalization of a product measure
Let $(X,\mathfrak B(X))$ and $(Y,\mathfrak B(Y))$ be measurable spaces and further let $\mu$ be a measure on $\mathfrak B(X)$ and let $K$ be a kernel, i.e. for any $x\in X$ we have $K_x$ is a measure ...
4
votes
1answer
140 views
Inverse function notation
Suppose $f$ and $g$ are functions that fail to be one-to-one, but $f+g$ is one-to-one. Has anyone ever seen the notation $(f+g)^{-1}$ for the inverse function in that situation? (I find myself ...
1
vote
1answer
120 views
Logic about systems?
In Godel's Incompleteness Theorem, his theorem is about a system of logic. Where can I find more about this study, especially the notation?
EDIT
I mean logic about systems in general. I worded the ...
3
votes
2answers
101 views
Original papers on the subject of group actions
Does anyone if there are any original paper(s) that first introduced the notion of group action or permutation representation, and who the author(s) were? Any references I have found so far on e.g. ...
3
votes
2answers
84 views
Relation-preserving maps as morphisms of a category
What is the canonical name for the category whose objects are all pairs $(X, \rho)$, where $X$ is a set and $\rho$ is a binary relation on $X$, and whose objects are relation-preserving maps? That is, ...
0
votes
2answers
100 views
Weak Partial Complete Lattice and Homomorphisms
What is the proper nomenclature for a generalization of a lattice $L$ such that not all subsets of $L$ may have a join/meet, sometimes not even for finite subsets? This paper calls it a "weak partial ...
3
votes
2answers
89 views
Textbook determinant convention
My text book is called "Linear Algebra and its applications" by David C. Lay.
I am just wondering why the textbook uses the absolute value symbol when it wants us to compute determinants. For ...
