## Kaori Yamazaki

*A proof for the Blair-Hager-Johnson theorem on absolute $z$-embedding *

Comment.Math.Univ.Carolinae 43,1 (2002) 175-179. **Abstract:**In this paper, a simple proof is given for the following theorem due to Blair [7], Blair-Hager [8] and Hager-Johnson [12]: A Tychonoff space $X$ is $z$-embedded in every larger Tychonoff space if and only if $X$ is almost compact or Lindel\"of. We also give a simple proof of a recent theorem of Bella-Yaschenko [6] on absolute embeddings.

**Keywords:** absolute $z$-embedding, absolute $C$-embedding, absolute $C^*$-embedding, absolute embeddings, almost compact, Lindel\"of, compact, pseudocompact

**AMS Subject Classification:** 54C25, 54D20

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