Pseudocompact spaces

Stephenson, R. M.

doi:10.1090/s0002-9947-1968-0232349-6

Cited by 19 publications

(4 citation statements)

References 12 publications

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“…Let X be a pseudo-compact topological space and let !£ be the lattice of zero-sets of X If $&(5£) is the algebra generated by 5£, a bounded set function J UL : M{5£) -> R is called ^-regular if JUL(A) = sup{fx(L) : L 6 if, L^A} for all Aes£(J£). Using the characterizations of pseudo-compactness [17,Theorem 2.3,p. 438], it is easily seen that the above mentioned lemma of Millington contains the following result of Glicksberg [7, pp.…”

Section: Monocompact Additive Set Functionmentioning

confidence: 99%

On Uniform Semigroup-Valued Additive Set Functions

Fox

Morales

1983

Can. math. bull.

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The main results of this paper are the following: (1) An extension theorem for a uniform semigroup-valued measure on a ring to the generated σ-ring. This result unifies the classieal Hahn-Carathéodory theorem, the extension theorem of Sion and a more recent result of Weber.(2) A theorem stating that every monocompact additive uniform semigroup-valued set function on a semiring is σ-additive. This result generalizes several earlier theorems of Alexandroff, Dinculeanu-Kluvanek, Glicksberg, Huneycutt, Mallory, Marczewski, Millington and Topsøe.

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Section: Monocompact Additive Set Functionmentioning

confidence: 99%

On Uniform Semigroup-Valued Additive Set Functions

Fox

Morales

1983

Can. math. bull.

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“…[1][2][3][4] Martensitic steels are usually quenched and tempered to improve their mechanical properties for use in various applications. 5) However, the elastic limit (EL) and yield strength (YS, 0.2% proof strength) of as-quenched martensitic steels are low, and thus are the subject of extensive research. 2,5) In past studies, strain aging or tempering at lower temperatures were investigated with the aim of increasing the YS.…”

Section: Introductionmentioning

confidence: 99%

“…5) However, the elastic limit (EL) and yield strength (YS, 0.2% proof strength) of as-quenched martensitic steels are low, and thus are the subject of extensive research. 2,5) In past studies, strain aging or tempering at lower temperatures were investigated with the aim of increasing the YS. 6,7) Here, applying a small amount of pre-strain followed by tempering at low temperatures (strain aging) is called strain tempering (ST).…”

Section: Introductionmentioning

confidence: 99%

Change in Mechanical Properties of High-Strength Martensitic Steel by the Combination of Pre-strain and Deformation Temperature

Tsuchida,

Kuramoto,

Ueji

et al. 2024

ISIJ Int.

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The effects of pre-strain on the mechanical properties of high-strength martensitic steels were investigated using either strain tempering (ST) or quenching and tempering (QT) samples. In the tensile tests at deformation temperatures between 296 and 573 K, the ST sample exhibited an increase in both the tensile strength (TS) and uniform elongation (U.El) at 473 to 523 K, whereas the QT sample showed an increase in U.El with little change in the TS and yield strength (YS). The results of in situ neutron diffraction experiments revealed an increase in the stress partitioning to the bcc phase with an increase in the deformation temperature from 296 to 523 K. The difference in the phase stress between the bcc and cementite phases decreased with an increase in the temperature due to the decrease in the cementite strength. Pre-strain of 0.5% increased the YS at 296 K with a slight work hardening; the initial dislocation density (ρ) decreased at 523 K, but increased significantly after yielding, leading to a better combination of TS and U.El. The combination of pre-strain, tempering, and deformation temperatures caused the change in ρ before deformation and the increase in ρ after yielding of the martensitic steel.

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“…Completely regular pseudocompact spaces have been studied extensively by Hewitt (1948), Glicksberg (1952Glicksberg ( , 1959, Bagley et al (1958), Frolik (1960), Gillman and Jerison (1960), Scarborough and Stone (1966) and Comfort (1967) among others. By comparison, until recently, pseudocompact spaces which are not necessarily completely regular had been studied primarily by Stephenson (1968). The author (1978) has recently studied such spaces.…”

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confidence: 99%