Titlebook: Rings of Continuous Functions; Leonard Gillman,Meyer Jerison Textbook 1960 Springer-Verlag New York 1960 Compactification.algebra.class.fu

晚來的提名

,The Stone-?ech Compactification,lready succeeded in obtaining characterizations in case . is compact—by attaching each maximal ideal to a point of the space (see 4.9(a)). The next step in our program is to extend this result, somehow, to the case of arbitrary (completely regular) .. In the general situation—when . is not pseudocom

colloquial

Characterization of Maximal Ideals,ter. The key to the description of the maximal ideals in .) has already been given: .) is isomorphic with .), and the maximal ideals in the latter ring are in one-one correspondence with the points of ..

ELUDE

外表讀作

Emmenagogue

abstemious

Discrete Spaces. Nonmeasurable Cardinals,alcompact. The question arises whether . discrete spaces are realcompact. Since, among discrete spaces, the cardinal is the only significant variable, this is, in fact, a question about cardinal numbers.

吸氣

Hyper-Real Residue Class Fields,). Although none of the material developed after Chapter 5 will be called upon, we shall need quite a bit more of the abstract theory of fields than heretofore. We begin with a summary of these algebraic prerequisites.

glowing

Prime Ideals,heorem 5.5), and hence that the canonical homomorphism .) of . onto . is a lattice homomorphism as well. Moreover, the integral domain . is totally ordered. The set of images of the constant functions is a copy of ., and we identify this copy with . itself.

Offbeat

Vsd168

,The Stone-?ech Compactification,ep in our program is to extend this result, somehow, to the case of arbitrary (completely regular) .. In the general situation—when . is not pseudocompact— we will be faced with two distinct problems: that of ., and that of ..