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AN EXTENSION WHICH IS A WEAKLY LINDELÖFF SPACE
Kim, Chang-Il
Abstract
In this paper, we construct an extension (<TEX>$kX$</TEX>, <TEX>$k_X$</TEX>) of a space X such that <TEX>$kX$</TEX> is a weakly Lindel<TEX>$\ddot{o}$</TEX>ff space and for any continuous map <TEX>$f:X{\rightarrow}Y$</TEX>, there is a continuous map <TEX>$g:kX{\rightarrow}kY$</TEX> such that <TEX>$g|x=f$</TEX>. Moreover, we show that <TEX>${\upsilon}X$</TEX> is Lindel<TEX>$\ddot{o}$</TEX>ff if and only if <TEX>$kX={\upsilon}X$</TEX> and that for any P'-space X which is weakly Lindel<TEX>$\ddot{o}$</TEX>ff, <TEX>$kX={\upsilon}X$</TEX>.
- keywords
- filter, realcompactification, weakly Lindel<tex> $\ddot{o}$</tex>ff space
Reference
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