# Tagged Questions

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### Criteria to judge te quality of a journal [migrated]

Is a journal with high impact factor is better than that with low impact factor? Is impact factor is right criteria to judge the quality of a journal?
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### Topological groups, why need them?

I'm reading through Munkres and Armstrong's books on topology. However, I find topological groups to be really complicated objects! I feel they are twice as hard to deal with then just groups and ...
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### Struggling with Topology. Any advice?

I'm a Junior Mathematics major at a small Liberal Arts college. I'm currently taking first semester topology (Munkres text). I feel like I'm barely able to tread water in this course. I was able to ...
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### Soft question: is there a generalization of compactness satisfying these conditions?

A good intuition about compact topological spaces is that they're spaces that aren't missing any points (not really a huge fan of the "compact = small" intuition, but that's another story). ...
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### Algebraic Object in Topology

Common algebraic categories are group, ring, module and algebra. Some of them have the corresponding object in topology, like topological group and topological linear space. We define them by making ...
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### Categorical introduction to Algebra and Topology

I am self-studying Mathematics in my free time. At the moment I am reading books on Algebra and on Category theory. More exactly, I started working through the book $\textit{Algebra}$ by Serge Lang. I ...
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### Are continuous mathematical models of discrete physical phenomena messy because of a disconnect between “continuous” and “discontinuous”?

Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the constituents of the system to which it applied ...
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### Metric Topology

Suppose our topological space is $\mathbb{R}$. Why is each basis element $(a,b)$ for the order topology is a basis element for the metric topology? Munkres says, ...
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### What is the contribution of group theory to topology?

An answer for a question on MathOverflow.net which asked for some recommendations on textbooks for books in topology received the following comment: "It's a great book to introduce applied ...
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### How can you describe topology to a non-mathematician without using continuous deformations?

One of the most frequently used ways to describe topology to non-mathematicians is that it studies the properties of objects that are preserved under deformations where ripping or tearing is not ...
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So, this is definitely a soft question and I apologize. I've been in point set topology for about a week and I have two questions, Everything spews from definition, so should I dismiss my geometric ...
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### Motivation for introducing algebraic topology?

What kind of topological questions does algebraic topology answer where point set topology is not enough? Phrased differently: Where is the line (or maybe intersection) between point set topology ...
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### 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 ...
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### How much topology for graph theory?

I am writing a thesis in the context of descriptive complexity in theoretical computer science and therefore need to study a little bit of graph theory. My background is not mathematics but computer ...
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### What's so cool about local compactness?

As I study more algebraic number theory, I hear more and more often about local compactness: locally compact fields, locally compact topological groups, Stone-Čech compactification of locally compact ...
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### How to develop intuition in topology?

Is there any efficient trick (besides doing exercises) to develop intuition in topology? The question is general but i would like to add my view of things. I started to teach myself topology through ...
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### 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 ...
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### A little confusion about compactness and connectedness

This question may be a bit simple or even naive for some people but it indeed confuses me for a long time. Thank you all if you provide any explanation. I know concepts: compactness means any open ...
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### What is the significance of limit points?

When I had my first taste of topology a couple of years ago, our lecturer emphasized the following notions. closed set, closure, closure point open set, interior, interior point Of course, these ...
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### Is my general approach to proofs acceptable? A general topology example.

Proving: $A$ is closed iff $A = \bar{A}$. "To the right": If $A$ is closed, $A = \bar A$ If $A$ is closed this means that it contains all of its own accumulation points. And we would find that its ...
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### Importance of Banach fixed point in mathematics

I know the proof of Banach fixed point theorem in complete metric space and two example of it. It is useful to prove Picard's theorem on existence and uniqueness of ordinary differential equation. In ...
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### Why is compactness so important?

I've read many times that 'compactness' is such an extremely important and useful concept, though it's still not very apparent why. The only theorems I've seen concerning it are the Heine-Borel ...
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### Can we get un-obvious results by defining sophisticated topologies?

What I originally found so interesting about general topology was how general a type of thing a topology is, and how the terminology open, closed, compact, continuous, convergence et cetera means ...
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