Point-set Topology

e-books in Point-set Topology category

Algebraic General TopologyAlgebraic General Topology
by Victor Porton - Mathematics21.org , 2015
I introduce the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces. Funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details concept of uniformity.
Metric and Topological SpacesMetric and Topological Spaces
by T. W. Körner - University of Cambridge , 2014
Contents: What is a metric?; Examples of metric spaces; Continuity and open sets for metric spaces; Closed sets for metric spaces; Topological spaces; Interior and closure; More on topological structures; Hausdorff spaces; Compactness; etc.

Point-Set Topology: CoursePoint-Set Topology: Course
by Peter Saveliev - Intelligent Perception , 2014
This is an introductory, one semester course on point-set topology and applications. Topics: topologies, separation axioms, connectedness, compactness, continuity, metric spaces. Intended for advanced undergraduate and beginning graduate students.
Quick Tour of the Topology of RQuick Tour of the Topology of R
by StevenHurder, DaveMarker - University of Illinois at Chicago , 2003
These notes are a supplement for the 'standard undergraduate course' in Analysis. The aim is to present a more general perspective on the incipient ideas of topology encountered when exploring the rigorous theorem-proof approach to Calculus.
Notes on Introductory Point-Set TopologyNotes on Introductory Point-Set Topology
by Allen Hatcher - Cornell University , 2011
These are lecture notes from the first part of an undergraduate course in 2005, covering just the most basic things. From the table of contents: Basic Point-Set Topology; Connectedness; Compactness; Quotient Spaces; Exercises.
General TopologyGeneral Topology
by Pierre Schapira - Université Paris VI , 2011
The aim of these lecture notes is to provide a short and self-contained presentation of the main concepts of general topology. Table of contents: Topological spaces; Metric spaces; Compact spaces; Banach spaces; Connectness and homotopy.
Nonstandard Analysis in TopologyNonstandard Analysis in Topology
by Sergio Salbany, Todor Todorov - arXiv , 2011
We present Nonstandard Analysis in the framework of the superstructure of a given infinite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics seem to be new in the literature.
by David Wilkins - Trinity College, Dublin , 2001
The lecture notes for course 212 (Topology), taught at Trinity College, Dublin. Topics covered: Limits and Continuity, Open and Closed Sets, Metric Spaces, Topological Spaces, Normed Vector Spaces and Functional Analysis, Topology in the Plane.
Introduction to TopologyIntroduction to Topology
by Alex Kuronya , 2010
Contents: Basic concepts; Constructing topologies; Connectedness; Separation axioms and the Hausdorff property; Compactness and its relatives; Quotient spaces; Homotopy; The fundamental group and some applications; Covering spaces; etc.
General TopologyGeneral Topology
by Jesper M. Moller , 2010
These notes are an introduction to general topology. They should be sufficient for further studies in geometry or algebraic topology. The text covers: Sets and maps; Topological spaces and continuous maps; Regular and normal spaces; etc.
Homeomorphisms in AnalysisHomeomorphisms in Analysis
by Casper Goffman, at al. - American Mathematical Society , 1997
This book features the interplay of two main branches of mathematics: topology and real analysis. The text covers Lebesgue measurability, Baire classes of functions, differentiability, the Blumberg theorem, various theorems on Fourier series, etc.
Elementary TopologyElementary Topology
by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov - American Mathematical Society , 2008
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space.
Topology Without TearsTopology Without Tears
by Sidney A. Morris , 2007
It provides a thorough grounding in general topology: introduction, topological spaces, the Euclidian topology, limit points, homeomorphisms, continuous mappings, metric spaces, compactness, finite products, countable products, Tychonoff's theorem.
A First Course in Topology: Continuity and DimensionA First Course in Topology: Continuity and Dimension
by John McCleary - American Mathematical Society , 2006
A focused introduction to point-set topology, the fundamental group, and the beginnings of homology theory. The text is intended for advanced undergraduate students. It is suitable for students who have studied real analysis and linear algebra.
Real Variables: With Basic Metric Space TopologyReal Variables: With Basic Metric Space Topology
by Robert B. Ash - Institute of Electrical & Electronics Engineering , 2007
A text for a first course in real variables for students of engineering, physics, and economics, who need to know real analysis in order to cope with the professional literature. The subject matter is fundamental for more advanced mathematical work.