# Tagged Questions

55 views

### Is “connected, simply connected” Redundant?

Here are my definitions of "connected" and "simply connected." A topological space $X$ is connected if and only if it is not the union of two nonempty disjoint open sets. A topological space ...
24 views

208 views

### Path components or connected components?

Can anyone explain the difference between these two terms? Are they basically different names for the same thing or totally different things?
41 views

### What are the names for the structures obtained when we drop some topological space axioms?

Motivation: If I start with the group axioms and drop the requirement that I have inverses, I get the monoid axioms. If I proceed to drop the requirement that I have an identity, I get the semigroup ...
580 views

### Why are compact sets called “compact” in topology?

Given a topological space $X$ and a subset of it $S$, $S$ is compact iff for every open cover of $S$, there is a finite subcover of $S$. Just curiosity: I've done some search in Internet why compact ...
95 views

### “clopen” terminology: acceptable?

I like the term "clopen" (a set which is both open and closed in a topological space), though an instructor of mine hated it when I used it recently. (Approximately, "never, ever use that again.") Is ...
43 views

### terminology needed

This is just a terminology question. Let $Y$ be a topological space. Is there a word to describe those topological spaces $X$ that contain $Y$ as a dense subspace? If not, what would you call such ...
49 views

### Quasicompact? Why the distinction?

What is the reason that some topologists use quasicompact? Why is the distinction made? quasi means "not really", so why use this terminology?
44 views

### What is the name for the topology where every point is in the boundary of an open set?

Is there a name for topological spaces in which every point is in the boundary of an open set?
91 views

### How to make a ghost manifold [closed]

How does one mathematically define a manifold that can pass through another manifold? A "ghost" passing through a "wall" type construction. I understand that this may be done by creating a copy of the ...
44 views

### Inverses of two argument functions with respect to one argument

Consider a function $f : A \times B \to C$ and two inverses, each with respect to one argument; i.e. $g$ and $h$ defined such that $f(x,y)=z \iff g(y,z)=x \iff h(z,x)=y$. A simple example is addition: ...
46 views

### The “standard” definition of discrete subspace

Let $X$ be a topological space and $D\subset X$ a generic subspace. In literature I have found the following different definitions: $D$ is discrete in $X$ if $X$ doesn't contain limit points of $D$. ...
53 views

### If $B$ is a cover of $A$, then do we say that $C$ is a subcover of $B$, or of $A$?

My textbook variously says both "subcover of $A$" and "subcover of $B$" to refer to a subcollection $C$ of the collection $B$ (that covers $A$); is this usage standard and is it not potentially ...