Characterization of the set-theoretical geometric realization in the non-Euclidean case
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- by Carlos Ruiz Salguero and Roberto Ruiz Salguero PDF
- Proc. Amer. Math. Soc. 81 (1981), 321-324 Request permission
Abstract:
A helpful feature in Milnorβs geometric realization [1] of a simplicial set $X$ is that each equivalence class admits one and only one element (optimal pair) of the form $(\bar x,\bar t)$ where $\bar x$ is nondegenerate and $\bar t$ is an interior point. This realization and several other aspects of Algebraic Topology admit generalizations (R. Ruiz [3]) changing the cosimplicial topological space of the ${\Delta ^n}$ by a general one, say $Y$. This paper is devoted to establishing conditions on $Y$ which guarantee the existence of such pairs on ${R_Y}(X)$ for every simplicial set $X$. ${R_Y}$ denotes the new realization via $Y$.)References
- John Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math. (2) 65 (1957), 357β362. MR 84138, DOI 10.2307/1969967
- C. Ruiz Salguero and Roberto Ruiz, Remarks about the Eilenberg-Zilber type decomposition in cosimplicial sets, Rev. Colombiana Mat. 12 (1978), no.Β 3-4, 61β82. MR 533712 R. Ruiz, Change of models in Top and ${\Delta ^ * }S$, Doctoral Thesis, Temple University, Philadelphia, Pennsylvania, 1975. C. Ruiz and R. Ruiz, Conditions over a "Realization" functor in order for it to commute with finite products (to appear).
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 321-324
- MSC: Primary 55U10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0593481-2
- MathSciNet review: 593481