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  • Introduction to Lebesgue measure and integration. Sample textbook: Real Analysis by H. L. Royden. || [[Review of the field and completeness axions]]
    549 bytes (62 words) - 14:06, 18 March 2023
  • MAT 3333 Fundamentals of Analysis and Topology. MAT 3333 Fundamentals of Analysis and Topology.
    4 KB (586 words) - 15:57, 25 March 2023
  • == The Absolute Value of a Real Number == ...f <math>a</math> is a real number, then we define the '''absolute value of the number <math>a</math>''' denoted <math>\mid a \mid</math> or <math>\mathrm{
    11 KB (1,976 words) - 13:18, 27 November 2021
  • = Subspace topology= ...he '''relative topology''', or the '''induced topology''', or the '''trace topology''').
    11 KB (1,955 words) - 14:30, 23 January 2022
  • ...oints, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods. ...e most general type of a mathematical space that allows for the definition of limits, continuity, and connectedness. Other spaces, such as Euclidean spac
    19 KB (3,169 words) - 09:58, 29 October 2021
  • ...red set is an open set, the blue set is its boundary set, and the union of the red and blue sets is a closed set.]] ...a metric space—that is, when a distance function is defined—open sets are the sets that, with every point {{mvar|P}}, contain all points that are suffici
    24 KB (4,147 words) - 16:13, 28 October 2021
  • [[Uniform Convergence of Sequences of Functions]] * [[The Cauchy Criterion for Convergence]] <!-- 3213-3.5 -->
    9 KB (1,029 words) - 16:37, 29 January 2022
  • ...very fixed "size" (where the meaning of "size" depends on the structure of the ambient space.) ...so used to mean relatively compact. These definitions coincide for subsets of a complete metric space, but not in general.
    9 KB (1,582 words) - 20:18, 13 November 2021
  • ...213. An introduction to complex variables, including elementary functions, line integrals, power series, residues and poles, and conformal mappings. Genera * Complex numbers and the complex plane.
    6 KB (816 words) - 11:00, 24 March 2023
  • ...notion of connected spaces (and their connected components) as well as to the separation axioms for topological spaces. There are various ways in which two subsets of a topological space ''X'' can be considered to be separated.
    6 KB (1,047 words) - 21:31, 29 January 2022
  • ...ic, the green path has length <math>6 \sqrt{2} \approx 8.49</math>, and is the unique shortest path.]] ...not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable.
    16 KB (2,652 words) - 14:31, 29 October 2021
  • The textbook(s) for this course is [1] Undergraduate Topology, by R. H. Kasriel; topics from [2] Introduction
    12 KB (1,471 words) - 15:09, 23 January 2022
  • ...|The abscissae ("x-coordinates") of the red circles are stationary points; the blue squares are inflection points.]] '''Critical point''' is a wide term used in many branches of mathematics.
    16 KB (2,821 words) - 17:17, 14 November 2021
  • ...ing the symbol '''R''' or <math>\mathbb{R}</math> and is sometimes called "the reals". ...of the complex plane, and the real numbers can be thought of as a part of the complex numbers.
    28 KB (4,634 words) - 16:18, 25 October 2021
  • ...gence; functions and function limits. Introduction to topology of the real line. Emphasis on theorem proving. ''Sample textbook'': Introduction to Real Analysis by Bartle and Sherbert
    8 KB (729 words) - 20:56, 24 March 2023
  • ==Types of maps between metric spaces== The map <math>f\,\colon M_1\to M_2</math> is continuous
    4 KB (724 words) - 13:10, 23 January 2022
  • ...ce'' between any two members of the set, which are usually called points. The metric satisfies a few simple properties. Informally: ...math>B</math> is zero if and only if <math>A</math> and <math>B</math> are the same point,
    29 KB (5,181 words) - 22:13, 26 October 2021
  • ==Definition and illustration of Hilbert Space== ...x'''}} and {{math|'''y'''}} are represented in Cartesian coordinates, then the dot product is defined by
    17 KB (2,752 words) - 14:34, 10 November 2021
  • <noinclude>{{navigation|Book=Topology ...esque and accessible; it will subsequently lead us to the full abstraction of a topological space.
    37 KB (6,977 words) - 16:54, 28 September 2021
  • ...tions as well, to provide some remarks of common functions that do not fit the bill. ...s on the domain <math>\R\setminus \{0\}</math>, but is not continuous over the domain <math>\R</math> because it is undefined at <math>x=0</math>]]
    21 KB (3,737 words) - 23:56, 5 November 2021

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