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| bio | website | pages.bangor.ac.uk/~mas013 |
|---|---|---|
| location | Ynys Mon, Cymru (i.e. Anglesey, Wales, UK) | |
| age | 65 | |
| visits | member for | 2 years, 1 month |
| seen | Feb 23 at 8:08 | |
| stats | profile views | 146 |
I was professor of mathematics at the University of Wales Bangor. The university shut the mathematics department. For more info. see my nLab page.
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Oct 3 |
answered | What should a math graduate know? |
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Jun 27 |
awarded | Enlightened |
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Jun 27 |
awarded | Nice Answer |
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Mar 24 |
awarded | Yearling |
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Jan 30 |
answered | A very vague question about the cartesian product in mathematics. |
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Jan 6 |
answered | Notes on dga's with a look towards Rational Homotopy Theory? |
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Dec 13 |
comment |
Is category theory useful in higher level Analysis? You might repost this question to MO as it may attract more replies there. Also there has been some mention of categories of Banach spaces, Banach bundles etc on discussions on the nForum and entries in the nLab, so have a look over there as well. |
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Sep 23 |
answered | What is a“canonical morphism” in a category? |
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Aug 24 |
awarded | Commentator |
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Aug 24 |
comment |
Domain, Co-Domain & Range of a Function One important reason for the use of codomain is if discussing properties of functions. $f:\mathbb{R}\to \mathbb{R}$, with $f(x)= x^2$ as above is not 'onto', whilst $f:\mathbb{R}\to [0,\infty)$, with $f(x)= x^2$ is. These two functions have different properties so must be different functions.:-), and the use of language where this point is not taken into account leads to a mess. It is also the case, of course, that domain and codomain then play roles that are nearer being dual to each other. |
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Aug 7 |
comment |
What is a rigorous proof of the topological equivalence between a donut and a coffee mug? The problem with the question is that neither the coffee cup nor the doughnut has been made that precise. In this case it is very difficult to give and explicit homeomorphism between them. On the other hand if you start with a mug without handle, specified as ever you like then it should be possible to produce a flat disc (thickness that of the mug) and then add a handle. (Is the torus a solid torus or just the surface... ditto for the mug?) |
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Aug 7 |
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What is a rigorous proof of the topological equivalence between a donut and a coffee mug? The point is that the topological equivalence will not preserve any cream filling, as that will flow all over the place unless thoroughly beaten. |
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May 2 |
answered | Shapes on a sphere's surface |
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May 1 |
comment |
Generator of a group How are you defining a generator of a group? It is more usual to refer to a generating set. The second part of your first question is more in that vein. In any case the answer will be yes and yes! (as was said below). |
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Apr 30 |
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Configuration space of three points in $\mathbb{R^{3}}$ There is an interesting discussion (in detail) of this in a book by David Kendall et al called Shape Theory. They discuss probability distributions on the configuration space and then the idea of a random triangle. |
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Apr 30 |
comment |
Time in Mathematics Of interest is the recent development of directed homotopy theory. This looks at non-reversible maps. It also interacts with Theoretical COmputer Science (TCS) see other answers. |
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Apr 28 |
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What is Cech homology? @Aaron The point is that those theorems are the 'smoothest' form of the story. On non-compact manifolds you need extra tools to handle the endspaces. On compact metric spaces you need extra tools to handle the local singularities. The theories are dual! On commutative $C^*$ algebras there is a homotopy theory and,surprise, it is related to those mentioned above. (What about non-commutative topological spaces?) CW-complexes were developed because of the possibility of a combinatorial homotopy theory, i.e. a fairly constructive form of the theory. It can be pushed much further. |
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Apr 28 |
comment |
What is Cech homology? My viewpoint has always been : as 'pathological' spaces arise naturally in other areas, I do not understand why algebraic topologists think of them as pathological. Another point is if someone starts a paper or discussion with ''given a space $X$..'' perhaps one should ask how is it 'presented'? Rarely is it given as set plus a topology. Somewhere along the line there is a gap in the presentation of topology and this may be counter to the health of the subject. |
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Apr 24 |
answered | the formulation of Nielsen-Schreier theorem: every subgroup of a free group is free |
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Apr 24 |
answered | What's more general than category theory? |
