**3**

votes

**2**answers

435 views

### What is a generalized limit?

In the proof of Lemma 1.3 in the paper "The ideal structure of a groupoid C* algebra", Journal of Operator Theory 1991 by Jean Renault, I found the notion of a generalized limit of a net without any ...

**-2**

votes

**1**answer

101 views

### How one can use a real math function on transaction in Hybrid Petri Net fundamental equation?

Say we have a simple HPN with 2 continuous places $A$ and $B$ and one transition. We want a transition not only add and substract $N$ marks from $A$ and add $M$ to $B$ but use mathematical function $...

**2**

votes

**1**answer

56 views

### Why is the doubling dimension of any net of a metric space at most half of that of the metric space?

Definition Doubling dimension ($\dim_D(M)=k$): A Metric space $M=(V,d)$ has doubling dimension at most $k$ if for any $x\in V$ & $r>0$, $B(x,r)\subseteq\bigcup^{2^k}_{i=1}B(x_i,r/2)$.
With ...

**2**

votes

**1**answer

101 views

### How does “inhibitor arc” fit into fundamental equation of Hybrid Petri Nets?

In "ON HYBRID PETRI NETS" by DAVID AND ALLA published in 2001 on page 26 is given an example of how fundamental equation solves a HPN for given start and end time values.
A system looks like
And ...

**2**

votes

**1**answer

103 views

### A quasicompact space with a net that contains no convergent strict subnet

If $x:\Lambda \rightarrow X$ is a net in a topological space $X$ and $\Lambda '\subseteq \Lambda$ is a cofinal subset of the directed set $\Lambda$, then $x|_{\Lambda '}$ is a subnet of $x$. We call ...

**7**

votes

**1**answer

349 views

### What should the morphisms in the Category of Directed Sets be?

Directed sets are defined to be sets equipped with a preorder that admit (finitary) upper bounds e.g. pairs $(D, \preceq)$ such that $\forall p,q \in D$ there exists $r \in D$ such that $p \preceq r$ ...

**5**

votes

**1**answer

280 views

### Connection between subnet and superfilter

Let's define a net and subnet in this way:
A net is any function of the form $n:(P,\le)\to X$ where $(P,\le)$ is a (preordered) directed set.
A net $m:(P',\le)\to X$ is a subnet of the net $n:(P,\le)...

**1**

vote

**0**answers

341 views

### Direct Limits and Limits of Nets

A net is a function from a directed set into a topological space, and it is said to converge to a point if certain conditions are satisfied. Similarly, a direct system is a function from a directed ...