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An Effective Tietze-Urysohn Theorem for QCB-Spaces

Matthias Schröder
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
Moreover, for qcb-spaces we introduce a slightly weaker notion of normality than the classical one and show that this property still admits an Extension Theorem for continuous functions.  ...  The Tietze-Urysohn Theorem states that every continuous real-valued function defined on a closed subspace of a normal space can be extended to a continuous function on the whole space.  ...  The effective Tietze-Urysohn Extension Theorem Now we are ready to formulate the effective Tietze-Urysohn Extension Theorem for quasi-normal qcb-spaces.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2008.12.020">doi:10.1016/j.entcs.2008.12.020</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uquxwigg3raepeai5rtpt6uxjm">fatcat:uquxwigg3raepeai5rtpt6uxjm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190219071706/https://core.ac.uk/download/pdf/82814342.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/08/1d/081d398c517b369e1583029073167fb4cc2e21ae.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2008.12.020"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

A Note on Closed Subsets in Quasi-zero-dimensional Qcb-spaces (Extended Abstract)

Matthias Schröder, Marc Herbstritt
<span title="2009-11-25">2009</span>
We introduce the notion of quasi-zero-dimensionality as a substitute for the notion of zero-dimensionality, motivated by the fact that the latter behaves badly in the realm of qcb-spaces.  ...  These results are related to an open problem in Computable Analysis.  ...  Acknowledgement I would like to thank the anonymous referees for their valuable suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/oasics.cca.2009.2274">doi:10.4230/oasics.cca.2009.2274</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vpactnqifnadjl3ppbzl3grsgq">fatcat:vpactnqifnadjl3ppbzl3grsgq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180518003736/http://drops.dagstuhl.de/opus/volltexte/2009/2274/pdf/Schroeder.2274.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/12/de/12de6ca5394da5b3c9dc8ba287f01c72ea982a6b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/oasics.cca.2009.2274"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

6th International Conference on Computability and Complexity in Analysis

Andrej Bauer, Peter Hertling, Ker-I Ko
<span title="">2009</span> <span class="release-stage">unpublished</span>
These proceedings contain the abstracts or extended abstracts of the invited talks, tutorials, and a selection of 22 contributed articles.  ...  In particular, Computable Analysis supplies an algorithmic foundation for numerical computation.  ...  The first author would like to thank the departments of mathematics of the University of Canterbury and the Universität Siegen for supporting him as an outgoing postdoctoral fellow and an incoming staff  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5qv7qlwnzbc7xiaeggl3ywsdzm">fatcat:5qv7qlwnzbc7xiaeggl3ywsdzm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180520043232/http://drops.dagstuhl.de/opus/volltexte/2012/3573/pdf/oasics-vol11-cca2009-complete.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fa/f7/faf73f6cf4d0ec56e14511fe128dd610feb73534.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>