MHB Example of right upper semicontinuous function

  • Thread starter Thread starter ozkan12
  • Start date Start date
  • Tags Tags
    Example Function
Click For Summary
Right upper semicontinuous functions are defined by the property that the upper limit of the function as x approaches a point from the right equals the function's value at that point. Common examples include the absolute value function f(x) = |x|, the exponential function f(x) = e^x, the logarithm function f(x) = log(x), the square root function f(x) = sqrt(x), and trigonometric functions like f(x) = sin(x) and f(x) = cos(x). These functions illustrate the concept of right upper semicontinuity effectively. Understanding these examples can aid in further research on the topic. Right upper semicontinuous functions play a significant role in various mathematical analyses.
ozkan12
Messages
145
Reaction score
0
I am researching right upper semicontinuous function but I didnt find...Please give some examples...thank a lot
 
Physics news on Phys.org
Right upper semicontinuous functions are functions that have the property that, for any x in the domain of the function, the upper limit of the function as x approaches that point from the right is equal to the value of the function at that point. Examples of right upper semicontinuous functions include:1) The absolute value function f(x) = |x|2) The exponential function f(x) = e^x3) The logarithm function f(x) = log(x)4) The square root function f(x) = sqrt(x)5) The trigonometric functions, such as f(x) = sin(x) and f(x) = cos(x)
 

Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
View full post »

Similar threads

MHB Is Limsup of Upper Semicontinuous Function True? Help Needed
  • · Replies 1 ·
Replies
1
Views
2K
Is F continuous if it is both upper and lower semicontinuous?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad In which sense(s) do square integrable functions go to zero at infinity?
  • · Replies 2 ·
Replies
2
Views
2K
Semicontinuity for single variable function. What is it all about?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Directional Derivatives .... Apostol, Section 12.2, Example 4 ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Complex Function Theory: Explaining Example 1.5, Section 1.2, Chapter III
  • · Replies 2 ·
Replies
2
Views
2K
MHB Upper and Lower Linits (lim sup and lim inf) - Denlinger, Theorem2.9.6 (b) ....
  • · Replies 4 ·
Replies
4
Views
2K
MHB Limit of upper semicontinuous function
  • · Replies 1 ·
Replies
1
Views
2K
MHB Where Does the Sign of n Matter in Palka's Examples?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Isometries .... Garling, Example 11.5.2 .... ....
  • · Replies 2 ·
Replies
2
Views
1K