# Questions tagged [examples]

The tag has no usage guidance.

424 questions
110 views

### Example of a manifold with positive isotropic curvature but possibly negative Ricci curvature

Is there any example of a manifold with a positive isotropic curvature but it possibly obtains a negative Ricci curvature at some point and the direction? If we see the definition of the positive ...
66 views

905 views

### Examples of set theory problems which are solved using methods outside of logic

The question is essentially the one in the title. Question. What are some examples of (major) problems in set theory which are solved using techniques outside of mathematical logic?
97 views

### Definition and examples of operator-stable distributions

I was trying to understand the basic ideas of the operator-stable distributions. I found the papers by Hudson and Sato. However, unfortunately, I am being unable to understand the mathematical ...
135 views

804 views

### Examples of residually-finite groups

One of the main reasons I only supervised one PhD student is that I find it hard to find an appropriate topic for a PhD project. A good approach, in my view, is to have on the one hand a list of ...
427 views

### Example of a smooth family of projective surfaces with non-vanishing integrals of Todd classes

Motivation: Let $\pi\colon S \rightarrow B$ be smooth projective morphism of relative dimension 2 over a smooth projective scheme $B$. If the stucture sheaves of the fibres do not have higher ...
166 views

### Naturally occurring, non-amenable Zappa-Szep products of discrete amenable groups?

We say $G$ is the Zappa-Szep product of two subgroups $K$ and $P$ if $K\cap P = \{e\}$ and the function $K\times P \to G$, $(k,p)\mapsto kp$, is bijective. The Iwasawa decomposition shows that we can ...
134 views

### Isolated periodic trajectories of Hamiltonian systems

Is there any example of an autonomous Hamiltonian system with a periodic trajectory isolated in the whole phase space? The Poincar\'e map of such a trajectory within its energy level should be very ...
180 views

### How could I see quickly that this space is not normal?

Recently, I read a paper in which the author construct a space $X$ which is dense in a $\sigma$-product $S$ of closed unit intervals. The space $X$ is CCC (denotes countable chain condition); it is ...
113 views

### Let $X$ be a Lindelof, perfectly normal, $\sigma$-space. Must $X$ be separable?

A space $X$ is a $\sigma$-space if $X$ has a $\sigma$-discrete network. Let $X$ be a Lindelof, perfectly normal, $\sigma$-space. Must $X$ be separable? Thanks very much.
904 views

### For each $n$: show there is a genus $1$ curve over some field $k$ with no points of degree less than $n$, (simple argument / best reference)?

What is the simplest example (or perhaps best reference) for the fact that there are genus $1$ curves (over a field of your choice --- or if you wish, over $\mathbb{Q}$, to make it more exciting) with ...
165 views

### Applications of logic in theoretical and practical Computer Science [closed]

Can anyone suggest theoretical and/or practical applications of logic (modal, dynamic, Lukasiewici etc.) in Computer Science (like Markov Chains for linear algebra), as well as some open-source books ...
138 views

### Non-homogeneous space $X$ such that $X\cong X\setminus \{x\}$ for all $x\in X$

What is an example of a topological space $(X,\tau)$ with the properties that $X\cong X\setminus \{x\}$ for all $x\in X$, and $(X,\tau)$ is not topologically homogeneous ?
127 views

396 views

### Example of Banach spaces with non-unique uniform structures

While it is known that compact Hausdorff spaces admit unique uniform structures, it is further shown by Johson and Lindenstrauss's result that Banach spaces are characterized by their uniform ...
122 views

### Semi-metrizable spaces with countable chain condition

Note that $X$ is semi-metrisable iff $X$ is first countable and semi-stratifiable. Definition A topological space $(X,\tau)$ is called semi-metric if there exists a function $g:\omega\times X\to\tau$...
381 views

2k views

### Consequences of the Birch and Swinnerton-Dyer Conjecture?

Before asking my short question I had made some research. Unfortunately I did not find a good reference with some examples. My question is the following What are the consequences of the Birch and ...
308 views

### Non-trivial examples of Stably diffeomorphic 4-manifolds

I am looking for some non-trivial examples of (smooth) 4-mflds $M,N$ such that $M$ and $N$ are STABLY diffeomorphic. I.e. $$M\sharp_n (S^2\times S^2) \cong N \sharp_r (S^2\times S^2)$$ for $r,n$ not ...
2k views

### Phenomena of Gerbes

What is your favourite example of Gerbes? I would like to know Where do we find Gerbes in "nature"? The examples could vary from String theory to Galois theory. For example my favourite examples of ...
239 views

### Is there a list of examples of orthogonal spectra?

Schwede's symmetric spectra book project provides point-set models of many important spectra as symmetric spectra, including (in §I.1) the sphere spectrum, Eilenberg-Mac Lane spectra, several Thom ...
179 views

### Is there a known construction for heavy topologies of all sizes?

Given a set $A$ is there a known way to find a topological space $X$ such that $|A|=|X|<w(X)$? Here $w(X)$ is the weight of the topological space. This is clearly impossible for finite sets $A$. ...
1k views

### Applications of logic to group theory?

There seems to be an ever-growing literature on the first-order theory of groups. While I find this interaction between group theory and logic quite appealing, I was wondering the following: Are ...
229 views

### An example of Guillemin Sternberg Conjecture

Guillemin Sternberg Conjecture(proved) says that for symplectic manifold $(M,\omega)$ with $[Q,R]=0$ condiction, with compact group action $G$, such that $\mu:M\to \mathfrak g^*$ is regular at $0$, ...