Specialization Definition and 7 Discussions

In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space. For most spaces that are considered in practice, namely for all those that satisfy the T0 separation axiom, this preorder is even a partial order (called the specialization order). On the other hand, for T1 spaces the order becomes trivial and is of little interest.
The specialization order is often considered in applications in computer science, where T0 spaces occur in denotational semantics. The specialization order is also important for identifying suitable topologies on partially ordered sets, as is done in order theory.

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  1. Alex Petrosyan

    Astrophysics vs Condensed Matter

    Hello everyone, I'm a Physics student on a gap year, doing a bit of work ATM. I'm going to come back in October this year to do a one-year Masters' at Cambridge, and I'm faced with a tough choice: A) Specialize in Astrophysics/cosmology, which is something that I'm not as good at, but really...
  2. S

    Programs Applied Physics specialization: Biophysics vs Quantum

    Hi! I am starting my Master's in Applied Physics at the TU Delft next week and I have yet to decide a research track (i.e. specialization). I have narrowed my options down to bionanoscience and quantum nanoscience. Of these two, which would be better? Of course, 'better' is a vague term, so what...
  3. ramzerimar

    Engineering Mechatronics or Thermal and Fluids for specialization?

    I'm a Mechanical Engineering student at the 4th semester, and I've been thinking about what specializations I should pursue after I get my bachelor's degree. I've always find mechatronics (control and automation) to be quite fun. I've developed some projects using Arduino and studied a little...
  4. D

    Programs Advice Request for a Fresh Physics Student

    Hi everyone, So to provide some background, I'm a 20 year old student in a community college who is about to transfer to a 4 year school in the coming winter. My interest in physics is fairly recent, as I was planning on becoming an astronomer when I entered college, but took an algebra based...
  5. ramzerimar

    Engineering Specialize yourself or be a Jack of all trades?

    I've been thinking about the potential benefits - or detriments - of specializing yourself in some particular field of work. Currently, I'm into Mechanical Engineering, and I've heard all kinds of arguments in that matter. Some say that specializing is good because you get better chance of most...
  6. D

    Possible to Specialize in General Relativity?

    I'm about to start my senior year at university pursuing a double major in physics and electrical engineering. I decided recently that I wanted to go to graduate school for physics so I started thinking about the area I would like to specialize in. My current university does most of its research...
  7. E

    Engineering General engineering with specialization in electrical

    Hi, I want to be an engineer but am not completely decided on what kind. I was wondering if I get a general engineering degree and get a specialization in electrical engineering, will this allow me to pursue a job as an electrical/electronics engineer out of college? Any help would be...