View source for Cube-like continuum

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''$n$-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====
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|valign="top"|{{Ref|Pa}}||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
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====Comments====
In the special case $n=1$, these continua are also called snake-like, see {{Cite|Bi}}.

In {{Cite|Pa}} 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====
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|valign="top"|{{Ref|Bi}}||valign="top"|  R.H. Bing,   "Snake-like continua"  ''Duke Math. J.'', '''18'''  (1951)  pp. 553–663
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