Two Constructive Embedding-Extension Theorems with Applications to Continuity Principles and to Banach-Mazur Computability Export

@misc{citeulike:960870, abstract = {We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space (CSM) without isolated points, X, in such a way that every sequentially continuous function from Cantor space to Z extends to a sequentially continuous function from X to R. The second asserts an analogous property for Baire space relative to any inhabited locally non-compact CSM. Both results...}, author = {Bauer, Andrej and Simpson, Alex}, citeulike-article-id = {960870}, citeulike-linkout-0 = {http://citeseer.ist.psu.edu/bauer03two.html}, citeulike-linkout-1 = {http://citeseer.lcs.mit.edu/bauer03two.html}, citeulike-linkout-2 = {http://citeseer.ifi.unizh.ch/bauer03two.html}, citeulike-linkout-3 = {http://citeseer.comp.nus.edu.sg/bauer03two.html}, keywords = {baire-space, baire-spaces, cantor-space, cantor-spaces, cardinality, sequence, sequence-spaces, sequences, topological-space, topological-spaces}, posted-at = {2009-06-24 22:37:21}, priority = {2}, title = {Two Constructive Embedding-Extension Theorems with Applications to Continuity Principles and to Banach-Mazur Computability}, url = {http://citeseer.ist.psu.edu/bauer03two.html} }

TY - GEN ID - citeulike:960870 L3 - citeulike-article-id:960870 N2 - We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space (CSM) without isolated points, X, in such a way that every sequentially continuous function from Cantor space to Z extends to a sequentially continuous function from X to R. The second asserts an analogous property for Baire space relative to any inhabited locally non-compact CSM. Both results... TI - Two Constructive Embedding-Extension Theorems with Applications to Continuity Principles and to Banach-Mazur Computability KW - baire-space KW - baire-spaces KW - cantor-space KW - cantor-spaces KW - cardinality KW - sequence KW - sequence-spaces KW - sequences KW - topological-space KW - topological-spaces AU - Bauer, Andrej AU - Simpson, Alex UR - http://citeseer.ist.psu.edu/bauer03two.html ER -