Full entry |
PDF
(0.5 MB)
Feedback

McCord homology; Korppi homology; $\mu $-homology; Vietoris homology; nonstandard analysis

References:

[1] Dowker, C.H.: **Homology groups of relations**. Ann. of Math. (2) 56 (1952), no. 1, 84–95. DOI 10.2307/1969768 | MR 0048030

[2] Garavaglia, S.: **Homology with equationally compact coefficients**. Fund. Math. 100 (1978), no. 1, 89–95. DOI 10.4064/fm-100-1-89-95 | MR 0494066

[3] Imamura, T.: **Nonstandard homology theory for uniform spaces**. Topology Appl. 209 (2016), 22–29, Corrigendum in DOI:10.13140/RG.2.2.36585.75368. DOI 10.1016/j.topol.2016.05.016 | MR 3523460

[4] Isbell, J.R.: **Uniform Spaces**. Mathematical Surveys and Monographs, vol. 12, American Mathematical Society, Providence, 1964. MR 0170323 | Zbl 0124.15601

[5] Korppi, T.: **A non-standard homology theory with some nice properties**. Dubrovnik VI - Geometric Topology, September–October 2007.

[6] Korppi, T.: **On the homology of compact spaces by using non-standard methods**. Topology Appl. 157 (2010), 2704–2714. DOI 10.1016/j.topol.2010.07.023 | MR 2725362

[7] Korppi, T.: **A new microsimplicial homology theory**. viXra:1205.0081, 2012.

[8] Mardešić, S., Segal, J.: **Shape Theory**. North-Holland Mathematical Library, vol. 26, North-Holland, Amsterdam-New York-Oxford, 1982. MR 0676973

[9] McCord, M.C.: **Non-standard analysis and homology**. Fund. Math. 74 (1972), no. 1, 21–28. DOI 10.4064/fm-74-1-21-28 | MR 0300270

[10] Robinson, A.: **Non-standard Analysis**. Studies in Logic and the Foundations of Mathematics, vol. 42, North-Holland, Amsterdam, 1966. MR 0205854

[11] Stroyan, K.D., Luxemburg, W.A.J.: **Introduction to The Theory of Infinitesimals**. Pure and Applied Mathematics, vol. 72, Academic Press, New York-San Francisco-London, 1976. MR 0491163

[12] Wattenberg, F.: **Nonstandard analysis and the theory of shape**. Fund. Math. 98 (1978), no. 1, 41–60. DOI 10.4064/fm-98-1-41-60 | MR 0528354