Compact Definition and 309 Threads

  1. G

    Compact sets and homeomorphisms

    Hi there. I'm taking a course in analysis and I was thinking about the relation between compact sets and homeomorphism. We know that if f is an onto and one-to-one homeomorphism then it follows that for every subset K: K is compact in M <=> f(K) is compact in N Now, does this go the...
  2. P

    How can you tell if a specific topological space is compact?

    eddo's thread got me thinking: How can you tell if a specific topological space is compact? It seems like it would be hard to do just starting with the definition of compactness.
    • PBRMEASAP
    • Thread
    • Compact Space Specific Topological
    • Replies: 5
    • Forum: Calculus
  3. E

    A function on a compact set is compact

    If f : U → R is continuous on U, and E ⊂ U is closed and bounded, then f attains an absolute minimum and maximum on E. How do you prove this theorem? I asked about this a while ago, but now I have a chance to redo the assignment and I need to fix my proof. I started by proving it for the 1...
    • eddo
    • Thread
    • Compact Function Set
    • Replies: 8
    • Forum: Calculus
  4. S

    Show whether S-omega is SC, CC, LPC, or compact

    :bugeye: This is a topology question. Does anybody have any suggestions on how to prove that a topological space X is COUNTABLY compact (i.e. every COUNTABLE open cover has a finite subcover), IF AND ONLY IF, EVERY NESTED SEQUENCE of closed nonempty subsets of X has a nonempty intersection...
  5. F

    Construct compact set of R with countable limit points

    Construct a compact set of real numbers whose limit points form a countable set.
  6. phoenixthoth

    Hints only please: compact iff bicompact

    I'd like hints only please. I have an analysis book and I could look up the proof myself but I'm trying to prove it myself as an exercise; so giving the full proof would be redundant as well as counterproductive to my own learning. X is a metric space. In this other book, K is compact iff...
  7. G

    Introducing Yourself to Compact and Non-Compact Lie Algebras

    Hi I'm looking for a guide to introduce muyself in the study of compact and non compact Lie algebras. Please take a minute to signal me some bibliography al the respect. Thank very much Guillom
  8. V

    Manufacturing compact pulsed microlaser source in blue/green

    can you list out the companies manufacturing compact pulsed microlaser source in blue/green wavelengths?
    • vani
    • Thread
    • Compact Manufacturing Source
    • Replies: 1
    • Forum: Optics
  9. K

    A compact car, mass of 725 kg, is moving at 100 km.hr.

    A compact car, mass of 725 kg, is moving at 100 km.hr. What is its momentum? At what velocity is the momentum of a larger car, mass 2175 kg, equal to that of the smaller car? this is what i have so far: p=725(100 km/hr) but i don't kno how to change km/hr into m/sec. And i don't know...
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