Domain of a Function | Open or Closed Interval?

  • Thread starter Thread starter Niles
  • Start date Start date
  • Tags Tags
    Domain Function
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
1 reply · 2K views
Niles
Messages
1,834
Reaction score
0

Homework Statement


Hi

If I have a function defined in one point only given by e.g.

f(x) = 2,

then is the function f defined on a open "interval" or a closed "interval"?
 

Discussion

Physics news on Phys.org
Simple answer: a single point is a closed interval.

Complicated answer: it depends on the topology you put on R.
 

Similar threads

Undergrad Should convex functions be defined on open or closed intervals?

  • junyoung
  • · Replies 4 ·
  • Calculus
Replies
4

A question regarding continuous function on a closed interval

  • aalma
  • · Replies 9 ·
  • Calculus and Beyond Homework Help
Replies
9

Interval notation of function's domain question

  • late347
  • · Replies 1 ·
  • Precalculus Mathematics Homework Help
Replies
1

Undergrad An open set can be a closed interval?

  • Demystifier
  • · Replies 12 ·
  • Topology and Analysis
Replies
12

Is an increasing monotonic function in a closed interval also continuous?

  • Lancelot1
  • · Replies 1 ·
  • Calculus
Replies
1

Domain and Range of a Function and Its Inverse- Polynomials

  • opus
  • · Replies 9 ·
  • Precalculus Mathematics Homework Help
Replies
9

Undergrad Differentiability in an open and closed intervals

  • bubblewrap
  • · Replies 4 ·
  • Calculus
Replies
4

Parameterizing closed intervals [a,b] with parameter t

  • Queens
  • · Replies 1 ·
  • Precalculus Mathematics Homework Help
Replies
1

Domain of a composite function

  • ilii
  • · Replies 4 ·
  • Precalculus Mathematics Homework Help
Replies
4

Inverse Function of Greatest Integer Function in a Given Domain

  • Cookiey
  • · Replies 3 ·
  • Precalculus Mathematics Homework Help
Replies
3