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alternative set theory; biequivalence vector space; $\pi$-equivalence; continuous function; set uniform equivalence; compact; dimensionally compact

References:

[G-Z 1985] Guričan J., Zlatoš P.: **Biequivalences and topology in the alternative set theory**. Comment. Math. Univ. Carolinae 26 (1985), 525-552. MR 0817825

[K-Z 1988] Kalina M., Zlatoš P.: **Arithmetic of cuts and cuts of classes**. Comment. Math. Univ. Carolinae 29 (1988), 435-456. MR 0972828

[M 1979] Mlček J.: **Valuations of structures**. Comment. Math. Univ. Carolinae 20 (1979), 681-696. MR 0555183

[M 1990] Mlček J.: **Some structural and combinatorial properties of classes in the alternative set theory (in Czech)**. habilitation Faculty of Mathematics and Physics, Charles University Prague.

[Sm 1987] Šmíd M.: **personal communication**.

[Sm-Z 1991] Šmíd M., Zlatoš P.: **Biequivalence vector spaces in the alternative set theory**. Comment. Math. Univ. Carolinae 32 (1991), 517-544. MR 1159799

[V 1979] Vopěnka P.: **Mathematics in the Alternative Set Theory**. Teubner-Verlag Leipzig. MR 0581368

[V 1979a] Vopěnka P.: **The lattice of indiscernibility equivalences**. Comment. Math. Univ. Carolinae 20 (1979), 631-638. MR 0555179

[Z 1989] P. Zlatoš: **Topological shapes**. Proc. of the 1st Symposium on Mathematics in the Alternative Set Theory J. Mlček et al. Association of Slovak Mathematicians and Physicists Bratislava 95-120.