# Tagged Questions

Deprecated; please use a more specific tag.

232 views

### Higher Homotopy groups [closed]

Are there topological spaces with non trivial homotopy groups $\pi_{>=2}$ that are visualizeable? I'm thinking about the the shape of what is called a "higher dimensional hole" but I can't find ...
453 views

### Ultrafilters and principal filters [closed]

Can someone give me an example of an ultrafilter which is not principal?
340 views

### Fine and acyclic sheaves on locales

Hey all. Here's the thing, so I have a measure space. According to Johnstone's 'Topos theory' (page 213), let $(X,\Sigma,\mu)$ be a measure space, we can define a Grothendieck pretopology on it (and ...
400 views

### Including a Jordan arc into a Jordan loop (Can the Magi go home by another way?)

The title refers, of course, to Matthew (2:12) ''And being warned in a dream not to return to Herod, they departed to their own country by another way''. To be honest, it is not that specific ...
312 views

### Topological space with some conditions

Can one give an example of non-compact space $X$ which satisfies the following conditions: the countable union of compact subsets is relatively compact, for every closed noncompact subset $A$ of $X$ ...
535 views

### Are presheaves of constant functions sheaves?

Hey there, I was reading 'An introduction to homological algebra' by Rotman, and on page 279 in the section about sheaves, example 5.64, Rotman gives an example of a constant presheaf $\mathcal{P}$ ...
263 views

### Borel bijection between Polish spaces [closed]

Let $X$ and $Y$ be two subsets of Polish spaces. Let $f:X\rightarrow Y$ be a bijection and borel measurable. How can one show that $f^{-1}$ is also borel measurable?
394 views

### What locally euclidean topological spaces are embeded in $\mathbb{R}^n$? [duplicate]

Possible Duplicate: Is there a Whitney Embedding Theorem for non-smooth manifolds? A topological space $X$ is locally Euclidean if for each $p\in X$ there is neighbourhood which is ...
350 views

### The topology of open semi-algebraic sets (appl.: totally positive matrices)

Let $P_1,\ldots,P_r$ be polynomials over ${\mathbb R}^N$. I am interested in the homotopy class of the semi-algebraic set defined by $$P_j(x_1,\ldots,x_N)>0,\qquad j=1,\ldots,r.$$ Is there a ...
702 views

### Direct product of filters

Product $a\times b$ of filters $a$ and $b$ is defined as the filter (on the set of binary relations) defined by the base $\{ A\times B | A\in a,B\in b \}$. I will denote the principal filter ...
530 views

### A question about measurable structures on function spaces

Hey, I was just wondering, I'm using some of Robert Aumann's ideas about measurable structures on function spaces (From his paper 'Borel structures for Function spaces': ...
411 views

### Morse theory and adiabatic limits

Let's start with a product manifold $M\times N$, with a product Riemannian metric $g_M\oplus g_N$. Consider a generic Morse function $f(x, y)$ on $M\times N$. Then its critical points are discrete and ...
10k views

### A good book of functional analysis

I'm a student (I've been studying mathematics 4 years at the university) and I like functional analysis and topology, but I only studied 6 credits of functional analysis and 7 in topology (the ...
894 views

748 views

### What kind of completion is this?

Let $X$ be a compact Hausdorff space, and $C(X)$ the unital commutative C*-algebra of continuous functions on it. The double Banach dual $C(X)^{**}$ is a commutative von Neumann algebra and hence has ...
344 views

### Homology of a region of the plane

This is related to this MO question, I don't know if it's really "research-level". As in that question, let $U$ be a domain of the complex plane $\mathbb{C}$, i.e. an open connected subset. Let ...
484 views

We are studying topology. There are a lot of definitions and theorems. I wonder if there somewhere knowledge base about topology and reasoning system exists. So I expect some tool that systematizes ...
133 views