View source for Cube-like continuum

$n$-cube-like continuum''

A compactum (metrizable compactum) admitting, for any $\epsilon > 0$, an $\epsilon$-mapping onto the ordinary cube $I^n$. If a compactum $X$ is the limit of a countable spectrum of compacta imbeddable in $I^n$, then $X$ is a subset of a cube-like continuum. The class of cube-like continua contains a universal element, i.e. a cube-like continuum $U$ such that every cube-like continuum is homeomorphic to some subspace of $U$.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  B.A. Pasynkov,   "On universal compacta"  ''Russian Math. Surveys'' , '''21''' :  4  (1966)  pp. 77–86  ''Uspekhi Mat. Nauk'' , '''21''' :  4  (1966)  pp. 91–100</TD></TR></table>



====Comments====
In the special case $n=1$, these continua are also called snake-like, see [[#References|[a1]]].

In [[#References|[1]]] it is shown that a space is $I^n$-like if and only if it is homeomorphic to the limit of an inverse sequence of copies of $I^n$ with surjective bounding mappings.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  R.H. Bing,   "Snake-like continua"  ''Duke Math. J.'' , '''18'''  (1951)  pp. 553–663</TD></TR></table>