View source for Dyadic space

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A [[Tikhonov space]] for which there is a [[compactification]] which is a [[dyadic compactum]]. The class of dyadic spaces contains all separable [[metric space]]s and is closed with respect to [[Tikhonov product]]s. Dyadic spaces display many of the properties of dyadic compacta. For instance, all pseudo-compact groups are dyadic, but non-dyadic finally compact groups exist. A dyadic space satisfies the [[Suslin condition]], but not every regular cardinal number $n\geq\mathbb{N}_{0}$ is the [[calibre]] of a dyadic space. Any regular closed set in a dyadic space is dyadic, but not all closed $G_\delta$ sets are. A dyadic space which satisfies the first axiom of countability is metrizable, but non-metrizable hereditarily normal, hereditarily separable dyadic spaces also exist.



====References====

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<TR><TD valign="top">[1]</TD> <TD valign="top">  V.I. Ponomarev,   "On dyadic spaces"  ''Fund. Math.'' , '''52''' :  3  (1963)  pp. 351–354  (In Russian)</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  B.A. Efimov,   "On dyadic spaces"  ''Soviet Math. Dokl.'' , '''4'''  (1963)  pp. 1131–1134  ''Dokl. Akad. Nauk SSSR'' , '''151''' :  5  (1963)  pp. 1021–1024</TD></TR>
</table>



====Comments====

Finally compact is usually termed Lindelöf in the West, cf. [[Lindelöf space]]. For regular closed set see [[Dyadic compactum]].