View source for Dominant of a topological space

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Any topological space for which <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033820/d0338202.png" /> serves as a retract (cf. [[Retract of a topological space|Retract of a topological space]]).



====Comments====
This is not standard Western terminology; there is in fact no name for this concept. The standard Western usage of dominating is as follows: A space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033820/d0338203.png" /> is said to dominate a space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033820/d0338204.png" /> if and only if there are continuous mappings <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033820/d0338205.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033820/d0338206.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033820/d0338207.png" /> is homotopic to the identity mapping (on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033820/d0338208.png" />).