Inverse Limits with Upper Semi-continuous Bonding Functions Whose Inverse Functions are Continuous
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DOI: 10.1007/s00009-020-01525-3
Abstract: In this paper, we investigate properties of inverse limits with upper semi-continuous bonding functions whose inverse functions are continuous. In particular, under the condition where each factor space is an arbitrary compactum, we give a… read more here.
Keywords: upper semi; continuous bonding; bonding functions; inverse limits ... See more keywords
On Direct and Inverse Limits of Retractive Spectra Once Again
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DOI: 10.1007/s10958-021-05240-6
Abstract: We prove that if an ∀∃-formula is true on the inverse limit of the retractive spectrum of algebras, then it is also true on the direct limit and establish some consequences for functions definable on… read more here.
Keywords: inverse limits; direct inverse; retractive spectra; limits retractive ... See more keywords
Inverse limits of Macaulay's inverse systems
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DOI: 10.1016/j.jalgebra.2019.01.024
Abstract: Abstract Generalizing a result of Masuti and the second author, we describe inverse limits of Macaulay's inverse systems for Cohen–Macaulay factor algebras of formal power series or polynomial rings over an infinite field. On the… read more here.
Keywords: inverse limits; inverse systems; macaulay inverse; limits macaulay ... See more keywords
Mahavier completeness and classifying diagrams
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DOI: 10.1016/j.topol.2017.07.007
Abstract: Abstract Generalised inverse limits of compacta were introduced by Ingram and Mahavier in 2006. The main difference between ordinary inverse limits and their generalised cousins is that the former concerns diagrams of singlevalued functions while… read more here.
Keywords: classifying diagrams; completeness classifying; mahavier limits; inverse limits ... See more keywords
Trees and generalised inverse limits on intervals
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DOI: 10.1016/j.topol.2018.09.006
Abstract: Abstract We consider inverse limits of sequences of upper semicontinuous set-valued functions f i + 1 : I i + 1 → 2 I i (where I i = [ 0 , 1 ] for… read more here.
Keywords: generalised inverse; topology; trees generalised; inverse limits ... See more keywords
Confluent projections and connectedness of inverse limits
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DOI: 10.1216/rmj.2021.51.1189
Abstract: V. Nall proved that connectedness is preserved under inverse limits if the bounding functions are unions of functions with connected images. We show that for such functions the projections from the graph onto domain are… read more here.
Keywords: inverse limits; confluent projections; connectedness inverse; projections connectedness ... See more keywords