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Let U be set of all n×n matrices A with complex enteries s.t. A is unitary. then U as a topological subspace of $\mathbb{C^{n^{2}}} $ is

  1. compact but not connected.
  2. connected but not compact.
  3. connected and compact.
  4. Neither connected nor compact

I am stuck on this problem . Can anyone help me please..... I don't know where yo begin........

  • 1
    This is a 2nd-3rd year in mathematics question. You've studied at least linear algebra and some topology: any thoughts, insights at all?2012-12-18
  • 0
    I read def. of connected and compact sets but don't know how to apply this........2012-12-18
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    Hint: Think of some continuous maps from $U$ and to $U$. There are some obvious choices of maps that have domain or codomain in the complex numbers (or a subset thereof).2012-12-18
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    still not getting sir........2012-12-18
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    please guide me sir......2012-12-18

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