# Countably evaluating homomorphisms on real function algebras

Eva Adam; Peter Biström; Andreas Kriegl

Archivum Mathematicum (1999)

- Volume: 035, Issue: 2, page 165-192
- ISSN: 0044-8753

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topAdam, Eva, Biström, Peter, and Kriegl, Andreas. "Countably evaluating homomorphisms on real function algebras." Archivum Mathematicum 035.2 (1999): 165-192. <http://eudml.org/doc/248362>.

@article{Adam1999,

abstract = {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.},

author = {Adam, Eva, Biström, Peter, Kriegl, Andreas},

journal = {Archivum Mathematicum},

keywords = {realcompactness; algebras of smoth functions; countably evaluating homomorphisms; realcompactness; algebras of smooth functions; countably evaluating homomorphisms},

language = {eng},

number = {2},

pages = {165-192},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Countably evaluating homomorphisms on real function algebras},

url = {http://eudml.org/doc/248362},

volume = {035},

year = {1999},

}

TY - JOUR

AU - Adam, Eva

AU - Biström, Peter

AU - Kriegl, Andreas

TI - Countably evaluating homomorphisms on real function algebras

JO - Archivum Mathematicum

PY - 1999

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 035

IS - 2

SP - 165

EP - 192

AB - 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.

LA - eng

KW - realcompactness; algebras of smoth functions; countably evaluating homomorphisms; realcompactness; algebras of smooth functions; countably evaluating homomorphisms

UR - http://eudml.org/doc/248362

ER -

## References

top- Smoothly realcompact spaces, Thesis, Univ. Vienna 1993.
- A real valued homomorphism on algebras of differentiable functions, Proc. Amer. Math. Soc. 90, 407–411 (1984). Zbl0694.46036MR0929406
- ${C}^{\infty}$-bounding sets and compactness, Math. Scand. 75, 82–86 (1994). MR1308939
- Algebras of real analytic functions; Homomorphisms and bounding sets, Stud. Math. 115, 23–37 (1995). MR1347430
- Homomorphisms on ${C}^{\infty}\left(E\right)$ and ${C}^{\infty}$-bounding sets, Monatsh. Math. 115, 257–266 (1993). MR1233957
- Characterizations of the spectra of certain function algebras, Archiv Math. 60, 177–181 (1993). MR1199676
- Function algebras on which homomorphisms are point evaluations on sequences, Manuscripta Math. 73, 179–185 (1991). MR1128686
- On compactness in locally convex spaces, Math. Z. 195, 365–381 (1987). MR0895307
- The weak topology of a Banach space, Trans. Amer. Math. Soc. 101, 1–15 (1961). Zbl0104.08502MR0132375
- The three space problem for smooth partitions of unity and $C\left(K\right)$-spaces, Math. Ann. 288, 613–625 (1990). MR1081267
- Measurability in a Banach space, II, Indiana Univ. Math. J. 28, 559–579 (1979). Zbl0418.46034MR0542944
- General topology, Berlin, Haldermann 1989. Zbl0684.54001MR1039321
- The dual of every Asplund space admits a projectional resolution of identity, Studia Math. 91, 141–151 (1988). MR0985081
- Linear Spaces and Differentiation Theory, Wiley 1988. MR0961256
- Homomorphisms on function algebras, Can. J. Math. 46, 734–745 (1994). MR1289057
- Rings of continuous functions, Springer 1960. MR0116199
- Banach space properties of Ciesielski-Pol’s $C\left(K\right)$ space, Proc. Amer. Math. Soc. 103, 1087–1093 (1988). MR0954988
- M-Ideals in Banach Spaces and Banach Algebras, Lecture notes in Mathematics, 1547. Springer 1993. MR1238713
- Locally convex spaces, Teubner 1981. Zbl0466.46001MR0632257
- Smoothness and its equivalents in weakly compactly generated Banach spaces, J. Functional Anal. 15, 1–11 (1974). MR0417759
- Characters on algebras of smooth functions, Ann. Global Anal. Geom. 7, 85–92 (1989). MR1032327
- More smoothly real compact spaces, Proc. Amer. Math. Soc. 117, 467–471 (1993). MR1110545
- Banach spaces and topology, in: Handbook of set theoretic topology (ed.: K. Kunen and J.E. Vaughan). North-Holland 1984. Zbl0832.46005MR0776619
- Smooth partitions of unity on some non-separable Banach spaces, Studia Math. T.XLVI, 43–51 (1973). MR0339255
- Topics in locally convex spaces, North-Holland 1982. Zbl0489.46001MR0671092

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