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realcompactness; algebras of smoth functions; countably evaluating homomorphisms
By studying algebra homomorphisms, which act as point evaluations on each countable subset, we obtain improved results on the question when all algebra homomorphisms are point evaluations.
[Ad] Adam, E.: Smoothly realcompact spaces. Thesis, Univ. Vienna 1993.
[Ar] Arias-de-Reyna, J.: A real valued homomorphism on algebras of differentiable functions. Proc. Amer. Math. Soc. 90, 407–411 (1984). MR 0929406 | Zbl 0694.46036
[BJ] Biström, P., Jaramillo, J.A.: $C^\infty $-bounding sets and compactness. Math. Scand. 75, 82–86 (1994). MR 1308939
[BJL] Biström, P., Jaramillo, J.A., Lindström, M.: Algebras of real analytic functions; Homomorphisms and bounding sets. Stud. Math. 115, 23–37 (1995). MR 1347430
[BL$_1$] Biström, P., Lindström, M.: Homomorphisms on $C^\infty (E)$ and $C^\infty $-bounding sets. Monatsh. Math. 115, 257–266 (1993). MR 1233957
[BL$_2$] Biström, P., Lindström, M.: Characterizations of the spectra of certain function algebras. Archiv Math. 60, 177–181 (1993). MR 1199676
[BBL] Biström, P., Bjon, S., Lindström, M.: Function algebras on which homomorphisms are point evaluations on sequences. Manuscripta Math. 73, 179–185 (1991). MR 1128686
[CO] Cascales, B., Orihuela, J.: On compactness in locally convex spaces. Math. Z. 195, 365–381 (1987). MR 0895307
[C] Corson, H. H.: The weak topology of a Banach space. Trans. Amer. Math. Soc. 101, 1–15 (1961). MR 0132375 | Zbl 0104.08502
[DGZ] Deville, R., Godefroy, G., Zizler, V.E.: The three space problem for smooth partitions of unity and $C(K)$-spaces. Math. Ann. 288, 613–625 (1990). MR 1081267
[Ed] Edgar, G.A.: Measurability in a Banach space, II. Indiana Univ. Math. J. 28, 559–579 (1979). MR 0542944 | Zbl 0418.46034
[En] Engelking, R.: General topology. Berlin, Haldermann 1989. MR 1039321 | Zbl 0684.54001
[FG] Fabian, M., Godefroy, G.: The dual of every Asplund space admits a projectional resolution of identity. Studia Math. 91, 141–151 (1988). MR 0985081
[FK] Frölicher, A., Kriegl, A.: Linear Spaces and Differentiation Theory. Wiley 1988. MR 0961256
[GGJ] Garrido, M.I., Gómez, J., Jaramillo, J.A.: Homomorphisms on function algebras. Can. J. Math. 46, 734–745 (1994). MR 1289057
[GJ] Gillman, L., Jerison, M.: Rings of continuous functions. Springer 1960. MR 0116199
[GPWZ] Godefroy, G., Pelant, J., Whitfield, J.H.M., Zizler, V.E.: Banach space properties of Ciesielski-Pol’s $C(K)$ space. Proc. Amer. Math. Soc. 103, 1087–1093 (1988). MR 0954988
[HWW] Harmand, P., Werner, D., Werner, W.: M-Ideals in Banach Spaces and Banach Algebras. Lecture notes in Mathematics, 1547. Springer 1993. MR 1238713
[J] Jarchow, H.: Locally convex spaces. Teubner 1981. MR 0632257 | Zbl 0466.46001
[JZ] John, K., Zizler, V.: Smoothness and its equivalents in weakly compactly generated Banach spaces. J. Functional Anal. 15, 1–11 (1974). MR 0417759
[KMS] Kriegl, A., Michor, P., Schachermayer, W.: Characters on algebras of smooth functions. Ann. Global Anal. Geom. 7, 85–92 (1989). MR 1032327
[KM] Kriegl, A., Michor, P.: More smoothly real compact spaces. Proc. Amer. Math. Soc. 117, 467–471 (1993). MR 1110545
[N] Negrepontis, S.: Banach spaces and topology. in: Handbook of set theoretic topology (ed.: K. Kunen and J.E. Vaughan). North-Holland 1984. MR 0776619 | Zbl 0832.46005
[T] Toruńczyk, H.: Smooth partitions of unity on some non-separable Banach spaces. Studia Math. T.XLVI, 43–51 (1973). MR 0339255
[V] Valdivia, M.: Topics in locally convex spaces. North-Holland 1982. MR 0671092 | Zbl 0489.46001
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