Point Set Topology With Topics:
Here, We provided to Point Set Topology With Topics By Robert Andre. In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology. Free download PDF Point Set Topology With Topics By Robert Andre.
The fundamental concepts in point-set topology are continuity, compactness, and connectedness:
- Continuous functions, intuitively, take nearby points to nearby points.
- Compact sets are those that can be covered by finitely many sets of arbitrarily small size.
- Connected sets are sets that cannot be divided into two pieces that are far apart.
The words ‘nearby’, ‘arbitrarily small’, and ‘far apart’ can all be made precise by using the concept of open sets. If we change the definition of ‘open set’, we change what continuous functions, compact sets, and connected sets are. Each choice of definition for ‘open set’ is called a topology. A set with a topology is called a topological space. Free download PDF Point Set Topology With Topics By Robert Andre.
Metric spaces are an important class of topological spaces where a real, non-negative distance, also called a metric, can be defined on pairs of points in the set. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces. Free download PDF Point Set Topology With Topics By Robert Andre.
Table Of Content:
- Norms and metrics
- Topological spaces: Fundamental concepts
- Topological spaces: Separation axioms
- Limit points in topological spaces
- Compact spaces and relatives
- The connected property
This text was prepared to serve as an introduction to the study of general topology. Most students in mathematics are required at some point in their study to have knowledge of some fundamentals of general topology since many of the tools and techniques mastered in that field will prove to be useful no matter what choice they make for their area of specialization. “Trust us, it will be good for you” they are told. But, sometimes, strange things happen. Free download PDF Point Set Topology With Topics By Robert Andre.
Some students develop a fascination for this field sometimes unfortunately described as being “no longer in fashion anymore”. Recall that the mathematicians, George Cantor and Felix Hausdorff, were also told that the area of mathematics they spent so much time investigating was, in their time, “not fashionable”. Reasons for the continued study of this topic often go beyond the simple perception that it is a practical or useful tool; the intricate beauty of the mathematical structures that are derived in this field become its main attraction. Free download PDF Point Set Topology With Topics By Robert Andre.
This is, of course, how this writer perceives the subject and served as the main motivation to prepare a textbook that will help the reader enjoy its study. Of course, one would at least hope that an author would write a book about something they are passionate about. But first, I should at least write a few words about the mathematical content of this textbook. The choice of content as well as the order and pace of the presentation of the concepts found in the text were developed with senior math undergraduate or math graduate students in mind.
The targeted reader will have been exposed to some mathematical rigor to a level normally found in an introduction to mathematical analysis texts or as presented in an introduction to linear algebra or abstract algebra texts. The first two sections consist mostly of a review of normed vector spaces and of a presentation of some very basic ideas on metric spaces. Free download PDF Point Set Topology With Topics By Robert Andre.
These are meant to ease the reader into the main subject matter of general topology. Once we have worked through the most fundamental concepts of topology in chapters one to twenty the reader will be exposed to various more specialized or advanced topics. These are presented in the form of five chapters where it is best to master one chapter before studying the following one. Free download PDF Point Set Topology With Topics By Robert Andre.
BOOK NAME – POINT SET TOPOLOGY WITH TOPICS
AUTHOR – ROBERT ANDRE
SIZE – 2.65MB
PAGES – 473
These chapters make excellent reading assignments for graduate students particularly if they are followed by in-class presentations so that other students can question and test the understanding of the presenter. A thorough understanding of the first twenty chapters is required. Each chapter is followed by a list of Concept review type questions. These questions highlight for students the main ideas presented in that section and will help test their understanding of these concepts.
The answers to all Concept review questions are in the main body of the text. Attempting to answer these questions will help the student discover essential notions that are often overlooked when first exposed to these ideas. Reading a section provides a certain level of understanding, but answering questions, even simple ones, related to its content requires a much deeper understanding. The efforts required in solving correctly various problems or exercise questions take the reader to where we want to go. Textbook examples will serve as solution models to most of the exercise questions at the end of each section. Free download PDF Point Set Topology With Topics By Robert Andre.
In certain sections, we make use of elementary set theory. A student who feels a bit rusty when facing the occasional references to set theory notions may want to review some of these. For convenience, a summary of the main set theory concepts appears at the end of the text in the form of an appendix to the book. More extensive coverage of naive set theory is offered in the book “Axioms and Set theory” by this writer. It is highly recommended and will serve as an excellent companion to this book. Free download PDF Point Set Topology With Topics By Robert Andre.
As we all know, any textbook, when initially published, will contain some errors, some typographical, others in spelling or in formatting and, what is even more worrisome, some mathematical. Many readers of the text are required to help weed out the most glaring mistakes. If you happen to be a reader who has carefully studied a chapter or two of the book please feel free to communicate to me, by email, any errors you may have spotted, with your name and chapters reviewed. In the preface of further versions of the book, I will gladly acknowledge your help. Free download PDF Point Set Topology With Topics By Robert Andre.
This will be much appreciated by this writer as well as by feature readers. It is always more pleasurable to study a book that is error-free. If an instructor wishes to use this book as the main textbook for his or her course and print bounded copies, please first obtain permission. Free download PDF Point Set Topology With Topics By Robert Andre.
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