How can I show that [tex]F:X\times I\to I[/tex] given by [tex]F(x,t)=(1-t)f(x)+tg(x)[/tex] is continuous, given that [tex]f:X\to I[/tex] and [tex]g:X\to I[/tex] are continuous (here I is the unit interval [0,1]). It seems that F is continuous, but I want to show that explicitly. Any help appreciated! X is any topological space.(adsbygoogle = window.adsbygoogle || []).push({});

(I wasn't sure what section to put this in - sorry!)

**Physics Forums - The Fusion of Science and Community**

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!

# X is any topological space

Loading...

Similar Threads for topological space | Date |
---|---|

Algebraic Topology: SO(3)/A5 | Jan 27, 2016 |

Topological properties on Linear spaces | Mar 18, 2009 |

X in dA => x isolated or strict limit (Topological space) | Mar 22, 2008 |

Colimits of topological spaces | Feb 19, 2007 |

Boundaries in topological space | Oct 24, 2005 |

**Physics Forums - The Fusion of Science and Community**