Hi, All:(adsbygoogle = window.adsbygoogle || []).push({});

I saw this question somewhere else: we are given any two topological spaces (X,T), (X',T'), and we want to see if there is always at least one continuous map between the two. The idea to say yes is this: we only need to find f so that f^{-1}(U)=V , for every U in T', and some V in T. So, it seems , for the infinite case, we could use choice to assign to each U in T' some V in T. Does this give us a well-defined map between (X,T) and (X',T')? It seems like we could then , similarly, define a measurable map between two measurable spaces using the same idea. Does this work?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Does there Exist a Continuous Map ?

Loading...

Similar Threads for Does Exist Continuous |
---|

B How does r∪(-p∩q∩-r) simplify to r∪(-p∩q) ? |

A Grouping Non-Continuous Variables |

A How does it not contradict the Cohen's theorem? |

A Why does Polychoric Reduce to two Factors? |

**Physics Forums | Science Articles, Homework Help, Discussion**