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data-folderul="Definitions/Topological-Spaces"><li><div class="folder-container"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="12" viewBox="5 8 14 8" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="folder-icon"><polyline points="6 9 12 15 18 9"></polyline></svg><div data-folderpath="Definitions/Topological-Spaces/Induced"><button class="folder-button"><span class="folder-title">Induced</span></button></div></div><div class="folder-outer "><ul style="padding-left:1.4rem;" class="content" data-folderul="Definitions/Topological-Spaces/Induced"><li><a href="./Definitions/Topological-Spaces/Induced/Initial-Topology" data-for="Definitions/Topological-Spaces/Induced/Initial-Topology">Initial Topology</a></li><li><a href="./Definitions/Topological-Spaces/Induced/Product-Topology" data-for="Definitions/Topological-Spaces/Induced/Product-Topology">Product Topology</a></li><li><a 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data-for="Definitions/Topological-Spaces/Terminologies/Compact">Compact</a></li><li><a href="./Definitions/Topological-Spaces/Terminologies/Connected" data-for="Definitions/Topological-Spaces/Terminologies/Connected">Connected</a></li><li><a href="./Definitions/Topological-Spaces/Terminologies/Connected-Component" data-for="Definitions/Topological-Spaces/Terminologies/Connected-Component">Connected Component</a></li></ul></div></li><li><a href="./Definitions/Topological-Spaces/Continuous" data-for="Definitions/Topological-Spaces/Continuous">Continuous</a></li><li><a href="./Definitions/Topological-Spaces/Hausdorff" data-for="Definitions/Topological-Spaces/Hausdorff">Hausdorff</a></li><li><a href="./Definitions/Topological-Spaces/Topological-Space" data-for="Definitions/Topological-Spaces/Topological-Space">Topological Space</a></li><li><a href="./Definitions/Topological-Spaces/Topology" data-for="Definitions/Topological-Spaces/Topology">Topology</a></li><li><a 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href="./Definitions/Vector-Spaces/Normed-Vector-Space" data-for="Definitions/Vector-Spaces/Normed-Vector-Space">Normed Vector Space</a></li><li><a href="./Definitions/Vector-Spaces/Properties-of-a-Vector-Space" data-for="Definitions/Vector-Spaces/Properties-of-a-Vector-Space">Properties of a Vector Space</a></li></ul></div></li><li><a href="./Definitions/Cauchy-Sequence" data-for="Definitions/Cauchy-Sequence">Cauchy Sequence</a></li><li><a href="./Definitions/Cauchy-Schwarz-Inequality" data-for="Definitions/Cauchy-Schwarz-Inequality">Cauchy-Schwarz Inequality</a></li><li><a href="./Definitions/Hilbert-Spaces" data-for="Definitions/Hilbert-Spaces">Hilbert Spaces</a></li><li><a href="./Definitions/Inner-Product" data-for="Definitions/Inner-Product">Inner Product</a></li><li><a href="./Definitions/Least-Upper-Bound-Property" data-for="Definitions/Least-Upper-Bound-Property">Least Upper Bound Property</a></li><li><a href="./Definitions/Linear-Map" data-for="Definitions/Linear-Map">Linear Map</a></li><li><a href="./Definitions/Nets" data-for="Definitions/Nets">Nets</a></li><li><a href="./Definitions/Norm" data-for="Definitions/Norm">Norm</a></li><li><a href="./Definitions/Number-Field" data-for="Definitions/Number-Field">Number Field</a></li><li><a href="./Definitions/Period-of-a-Fraction" data-for="Definitions/Period-of-a-Fraction">Period of a Fraction</a></li><li><a href="./Definitions/Rational-Cauchy-Sequences" data-for="Definitions/Rational-Cauchy-Sequences">Rational Cauchy Sequences</a></li><li><a href="./Definitions/Subcover" data-for="Definitions/Subcover">Subcover</a></li><li><a href="./Definitions/Subnet" data-for="Definitions/Subnet">Subnet</a></li></ul></div></li><li><div class="folder-outer "><ul style="padding-left:0;" class="content" data-folderul></ul></div></li><li><div class="folder-container"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="12" viewBox="5 8 14 8" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="folder-icon"><polyline points="6 9 12 15 18 9"></polyline></svg><div data-folderpath="Lectures"><button class="folder-button"><span class="folder-title">Lectures</span></button></div></div><div class="folder-outer "><ul style="padding-left:1.4rem;" class="content" data-folderul="Lectures"><li><a href="./Lectures/Lecture-1---1.1-Sets-and-Numbers" data-for="Lectures/Lecture-1---1.1-Sets-and-Numbers">Lecture 1 - 1.1 Sets and Numbers</a></li><li><a href="./Lectures/Lecture-2" data-for="Lectures/Lecture-2">Lecture 2</a></li><li><a href="./Lectures/Lecture-3" data-for="Lectures/Lecture-3">Lecture 3</a></li><li><a href="./Lectures/Lecture-4---1.2-Metric-Spaces" data-for="Lectures/Lecture-4---1.2-Metric-Spaces">Lecture 4 - 1.2 Metric Spaces</a></li><li><a href="./Lectures/Lecture-5" data-for="Lectures/Lecture-5">Lecture 5</a></li><li><a href="./Lectures/Lecture-6---2.1-Topology" data-for="Lectures/Lecture-6---2.1-Topology">Lecture 6 - 2.1 Topology</a></li><li><a href="./Lectures/Lecture-7" data-for="Lectures/Lecture-7">Lecture 7</a></li><li><a href="./Lectures/Lecture-8" data-for="Lectures/Lecture-8">Lecture 8</a></li><li><a href="./Lectures/Lecture-11" data-for="Lectures/Lecture-11">Lecture 11</a></li><li><a href="./Lectures/Lecture-12---Induced-Topologies" data-for="Lectures/Lecture-12---Induced-Topologies">Lecture 12 - Induced Topologies</a></li><li><a href="./Lectures/Lecture-13---Measure-Theory" data-for="Lectures/Lecture-13---Measure-Theory">Lecture 13 - Measure Theory</a></li></ul></div></li><li><a href="./ACIT4330-Lectures" data-for="ACIT4330-Lectures">ACIT4330 Lectures</a></li></ul></div></li><li id="explorer-end"></li></ul></div></div></div><div class="center"><div class="page-header"><div class="popover-hint"><nav class="breadcrumb-container" aria-label="breadcrumbs"><div class="breadcrumb-element"><a href="./">Home</a><p> ❯ </p></div><div class="breadcrumb-element"><a href>ACIT4330 Lectures</a></div></nav><h1 class="article-title">ACIT4330 Lectures</h1><p show-comma="true" class="content-meta"><time datetime="2025-03-01T12:58:10.778Z">Mar 01, 2025</time><span>1 min read</span></p></div></div><article class="popover-hint"><h1 id="chapter-1">Chapter 1<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#chapter-1" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h1>
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<h2 id="11-sets-and-numbers">1.1 Sets and Numbers<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#11-sets-and-numbers" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h2>
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<ul>
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<li><a href="./Lectures/Lecture-1---1.1-Sets-and-Numbers" class="internal alias" data-slug="Lectures/Lecture-1---1.1-Sets-and-Numbers">Lecture 1 - 1.1 Sets and Numbers</a> (complimentary written notes: <a href="./rnote/ACIT4330-2025-01-06-Lecture-1.rnote" class="internal alias" data-slug="rnote/ACIT4330-2025-01-06-Lecture-1.rnote">ACIT4330-2025-01-06-Lecture 1.rnote</a>)</li>
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<li><a href="./Lectures/Lecture-2" class="internal alias" data-slug="Lectures/Lecture-2">Lecture 2</a> (complimentary written notes: <a href="./rnote/ACIT4330-2025-01-09-Lecture-2.rnote" class="internal alias" data-slug="rnote/ACIT4330-2025-01-09-Lecture-2.rnote">ACIT4330-2025-01-09-Lecture 2.rnote</a>)</li>
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<li><a href="./Lectures/Lecture-3" class="internal alias" data-slug="Lectures/Lecture-3">Lecture 3</a></li>
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<li><a href="./Lectures/Lecture-4---1.2-Metric-Spaces#the-inverse-image" class="internal alias" data-slug="Lectures/Lecture-4---1.2-Metric-Spaces">The Inverse Image</a> and <a href="./Lectures/Lecture-4---1.2-Metric-Spaces#complex-numbers" class="internal alias" data-slug="Lectures/Lecture-4---1.2-Metric-Spaces">Complex Numbers</a>.</li>
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</ul>
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<h2 id="12-metric-spaces">1.2 Metric Spaces<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#12-metric-spaces" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h2>
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<ul>
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<li><a href="./Lectures/Lecture-4---1.2-Metric-Spaces" class="internal alias" data-slug="Lectures/Lecture-4---1.2-Metric-Spaces">Lecture 4 - 1.2 Metric Spaces</a></li>
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<li><a href="./Lectures/Lecture-5" class="internal alias" data-slug="Lectures/Lecture-5">Lecture 5</a></li>
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</ul>
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<h1 id="chapter-2">Chapter 2<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#chapter-2" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h1>
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<h2 id="21-topology">2.1 Topology<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#21-topology" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h2>
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<ul>
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<li><a href="./Lectures/Lecture-6---2.1-Topology" class="internal alias" data-slug="Lectures/Lecture-6---2.1-Topology">Lecture 6 - 2.1 Topology</a></li>
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<li><a href="./Lectures/Lecture-7" class="internal alias" data-slug="Lectures/Lecture-7">Lecture 7</a> (complimentary written notes: <a href="./rnote/ACIT4330-2025-01-30-Lecture-7.rnote" class="internal alias" data-slug="rnote/ACIT4330-2025-01-30-Lecture-7.rnote">ACIT4330-2025-01-30-Lecture 7.rnote</a>)</li>
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<li><a href="./Lectures/Lecture-8" class="internal alias" data-slug="Lectures/Lecture-8">Lecture 8</a></li>
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</ul>
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<h2 id="22-continuity">2.2 Continuity<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#22-continuity" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h2>
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<ul>
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<li><a href="./Lectures/Lecture-8" class="internal alias" data-slug="Lectures/Lecture-8">Lecture 8</a></li>
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<li><a href="./ACIT4330/Lectures/Lecture-11" class="internal alias" data-slug="ACIT4330/Lectures/Lecture-11">Lecture 11</a></li>
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<li><a href="./Lectures/Lecture-12---Induced-Topologies" class="internal alias" data-slug="Lectures/Lecture-12---Induced-Topologies">Lecture 12 - Induced Topologies</a></li>
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</ul>
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<h1 id="measure-theory">Measure Theory<a role="anchor" aria-hidden="true" tabindex="-1" data-no-popover="true" href="#measure-theory" class="internal"><svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></a></h1>
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<ul>
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<li><a href="./Lectures/Lecture-13---Measure-Theory" class="internal alias" data-slug="Lectures/Lecture-13---Measure-Theory">Lecture 13 - Measure Theory</a></li>
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