Point Set Topology
http://www.maa.org/taxonomy/term/41820/0
enAdvanced Plane Topology from an Elementary Standpoint
http://www.maa.org/programs/maa-awards/writing-awards/advanced-plane-topology-from-an-elementary-standpoint
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><b>Award:</b> Carl B. Allendoerfer</p>
<p><b>Year of Award:</b> 1981</p>
<p><b>Publication Information:</b> <i>Mathematics Magazine</i>, Vol. 53, (1980), pp. 81-89</p>
<p><b>Summary:</b> A simple combinatorial approach to subtle topological premises of basic undergraduate analysis.</p>
<p><a href="/sites/default/files/pdf/upload_library/22/Allendoerfer/1981/0025570x.di021114.02p00993.pdf">Link to Article</a></p></div></div></div>An Elementary Extension of Tietze's Theorem
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-elementary-extension-of-tietzes-theorem
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author proves several generalizations of Tietze's Theorem.</em></p>
</div></div></div>The Kuratowski Closure-Complement Problem
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-kuratowski-closure-complement-problem
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The Kuratowski closure-complement theorem states that starting with any subset A of a topological space, and alternately taking closures and complements of A, no more than 14 different sets are generated. </em></p>
</div></div></div>An Analysis of the First Proofs of the Heine-Borel Theorem
http://www.maa.org/press/periodicals/convergence/an-analysis-of-the-first-proofs-of-the-heine-borel-theorem
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>A comparison of circa 1900 proofs of the famous theorem with a view toward improving student understanding of compactness</p>
</div></div></div>A Characterization of the Set of Points of Continuity of a Real Function
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-characterization-of-the-set-of-points-of-continuity-of-a-real-function
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Let \(X\) be a nonempty metric space without isolated points. If \(G \) is a countable intersection of open sets, the author shows that there is a function \(\phi (x) \) that is continuous exactly on \(G\).</p>
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