On Volterra Spaces
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Youngstown State University / OhioLINK
2010
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=ysu1288364649 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-ysu12883646492021-08-03T06:17:54Z On Volterra Spaces Ballone, Frank Mathematics Volterra Volterra spaces Volterra's theorem <p>Continuity is one of the most important concepts in Mathematics. A. Cauchy wasone of the first to define the continuity of a function. Here is Cauchy's condition of the continuity of a function:</p><p>" ... We also say that the function <i>f(x)</i> is a continuous function of <i>x</i> in the neighborhood of a particular value assigned to the variable <i>x</i> as long as it (the function) is continuous between those two limits of <i>x</i>, no matter how close together, which enclose the value in question ... "(see [31]).</p><p>This concept was refined by K. Weierstrass, which is the definition of continuitythat we use today. For a historical account on how the notation of continuity hasevolved see [31].</p><p>The study of continuity usually begins in calculus, where we study continuousfunctions. Questions on how a set of points of continuity of a given real-valued function of real variable look are very important. I will discuss these sets for real-valued functions of real variable in chapter 1. In chapter 2, I will continue to look at real-valued functions and examine their points of continuity. This time, the functions will be defined on metric spaces. Furthermore, I will examine the set of points of continuity of real-valued functions defined on topological spaces in chapter 4. In chapter 3, important topological concepts are introduced that will be used from chapters 4 through 6.</p><p>The analysis of the existing proofs on the Volterra theorem, which I will begin todiscuss in chapter 1, led to the class of spaces known as <i>Volterra spaces</i>. In chapter 5, I will explain the concept of a Volterra space and explain various properties of these spaces. Finally, in chapter 6, I will list original and recent research results from various articles to illustrate the progress on Volterra spaces since their introduction in [15].</p><p>Throughout my thesis, I will illustrate various concepts with the help of diagramsand examples, some of I created. In addition, I will further explain topics fromclassical sources in detail to make the material easy to follow and more understandable to the reader.</p> 2010-11-02 English text Youngstown State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=ysu1288364649 http://rave.ohiolink.edu/etdc/view?acc_num=ysu1288364649 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
| collection |
NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics Volterra Volterra spaces Volterra's theorem |
| spellingShingle |
Mathematics Volterra Volterra spaces Volterra's theorem Ballone, Frank On Volterra Spaces |
| author |
Ballone, Frank |
| author_facet |
Ballone, Frank |
| author_sort |
Ballone, Frank |
| title |
On Volterra Spaces |
| title_short |
On Volterra Spaces |
| title_full |
On Volterra Spaces |
| title_fullStr |
On Volterra Spaces |
| title_full_unstemmed |
On Volterra Spaces |
| title_sort |
on volterra spaces |
| publisher |
Youngstown State University / OhioLINK |
| publishDate |
2010 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=ysu1288364649 |
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AT ballonefrank onvolterraspaces |
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