Homomorphisms from $$C(X,\mathbb {Z})$$ C ( X , Z ) into a ring of continuous functions

Olfati, A. R.

doi:10.1007/s00012-018-0509-9

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…Assume that the factor ring C(X, Z)/C F (X, Z) has a uniform ideal. Since by [9,Proposition 4.11], the factor ring C(X, Z)/C F (X, Z) is isomorphic with the ring C(X \ I(X), Z), it follows that the ring C(X \ I(X), Z) has an atomic ideal and hence by Proposition 2.6, the subspace X \ I(X) has an isolated point.…”

Section: Resultsmentioning

confidence: 99%

“…Equipped with the pointwise addition and multiplication of R X , the sets C(X, Z) and C c (X) form two subrings of C(X). The ring of integer-valued continuous functions have been studied in many ways and some outstanding results were achieved by some mathematicians, see for example [1], [6], [9] and [10]. Just recently in [2] an extensive study for the subalgebra C c (X) has been done.…”

Section: Introductionmentioning

confidence: 99%

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On atomic ideals in some factor rings of $C(X,\Bbb Z)$

Alireza¹

2021

Commentationes Mathematicae Universitatis Carolinae

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On atomic ideals in some factor rings of $C(X,\Bbb Z)$

Alireza¹

2021

Commentationes Mathematicae Universitatis Carolinae

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“…The inset map shows the extent of the Qilian Shan and the location of the study area. Strata information is based on 1:200,000 geological maps of China which from Ministry of Geology and Mineral Resources (Li et al., 2019).…”

Section: Study Areasmentioning

confidence: 99%

Tan DEM‐X Preserves the Relationship Between Hilltop Curvature and Erosion Rate in the Qilian Shan

Zhang,

Geng,

Cai

et al. 2023

JGR Earth Surface

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Hilltop curvature (CHT) can record erosional responses to tectonic forces and/or climate change. Although CHT has a linear relationship with the erosion rate, which is a significant advantage over traditional indicators, it is not widely used, mainly because it requires high‐resolution terrain data. Previous studies show that terrain steepness is strongly correlated with catchment‐wide erosion rates in the Qilian Shan. This relationship enables us to test the potential of CHT based on medium‐resolution terrain data (e.g., Tan DEM‐X with a resolution of ∼12 m) as an indicator of the erosion rate. We selected three typical sites in the Qilian Shan with evenly spaced ridge valleys and a continuous soil cover. At each site we produced a high‐resolution digital surface model (DSM) using uncrewed aerial vehicles (UAVs), and then compared CHT from the UAV DSM with that from Tan DEM‐X, via LSDTopoTools. The results show that both Tan DEM‐X and the UAV DSM record similar spatial patterns of CHT, although the magnitudes vary between the three selected areas. We then examined the relationship between CHT based on Tan DEM‐X and the catchment‐wide erosion rate in the Qilian Shan. CHT has a linear relationship with the erosion rate in an area of clastic rocks, where the erosion rate is below 400 mm/kyr. CHT extracted by Tan DEM‐X is superior to the mean basin slope in predicting the erosion rate in this clastic rock landscape. Overall, our results demonstrate the utility of Tan DEM‐X in calculating CHT to indicate the erosion rate.

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