The Structure of the Real Line

Bukovský, Lev

doi:10.1007/978-3-0348-0006-8

Cited by 35 publications

(30 citation statements)

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“…Similarly to [6], the empty set ∅ can be an element of a cover, but the whole space is not. If we consider enumeration of a cover, then we always assume that the set is repeated only finitely many times in the enumeration, i.e., the enumeration is adequate in the sense of [4]. An infinite cover A is a γ-cover if every x ∈ X lies in all but finitely many members of A.…”

Section: Preliminaries and Basic Notionsmentioning

confidence: 99%

“…Moreover, by A. Dow [15] Scheepers' Conjecture holds in the Laver model constructed by A. Laver [24], see e.g. [28,44] or [4].…”

Section: Upper Semicontinuous Functionsmentioning

confidence: 99%

“…[4], Theorem 3.70) a set of points of discontinuity of every F σ -measurable function on a separable metric space is meager. Hence we directly obtain that every F σ -measurable function on ℵ 1 -Luzin set 14 can be decomposed into countably many partial functions, each continuous on its domain.…”

Section: ) There Is a Borel Setmentioning

confidence: 99%

“…By a function we mean real-valued function. Basic set-theoretical and topological terminology follows mainly [4] and [16]. See [3,6,30] and our second section or footnotes for preliminary definitions.…”

Section: Introductionmentioning

confidence: 99%

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On Ohta–Sakai's properties of a topological space

Šupina

2015

Topology and its Applications

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We investigate modifications of properties USC s and LSC s introduced by H. Ohta and M. Sakai [30]. Our property wED(U , C(X)) holds in any S 1 (Γ, Γ)-space and property wED(L, C(X)) holds in perfectly normal QN-space. We present their covering characterizations and hereditary properties. Our main result is that a topological space X is an S 1 (Γ, Γ)-space if and only if X is both, a wQN-space and possesses wED(U , C(X)). Property wED(L, C(X)) is related to the condition "to be a discrete limit of a sequence of continuous functions" which is briefly studied in the paper as well. Moreover, for perfectly normal space we show that original property USCs is hereditary for Δ 0 2 subsets.

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Section: Preliminaries and Basic Notionsmentioning

confidence: 99%

“…Moreover, by A. Dow [15] Scheepers' Conjecture holds in the Laver model constructed by A. Laver [24], see e.g. [28,44] or [4].…”

Section: Upper Semicontinuous Functionsmentioning

confidence: 99%

Section: ) There Is a Borel Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Ohta–Sakai's properties of a topological space

Šupina

2015

Topology and its Applications

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“…in [7,Section 8.6]. While Dirichlet sets always have vanishing measure, they may be large in the sense that the Hausdorff dimension can be 1; see e.g.…”

Section: Proof (A) We First Note Thatmentioning

confidence: 99%

Banach Spaces of Universal Taylor Series in the Disc Algebra

Bernal–González

Jung

Müller

2016

Integr. Equ. Oper. Theory

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Abstract. It is proved that there are large vector spaces of functions in the disc algebra for which every nonzero member satisfies that, for many small subsets E of the unit circle T, the restrictions to T of the partial sums of its Taylor series at the origin approximate any prescribed function on E. Moreover, it is shown that such sets necessarily have to be small in terms of porosity.Mathematics Subject Classification (2010). Primary 47A16; Secondary 15A03, 40A30, 42A16, 46E10.

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Assessment of NARCCAP model in simulating rainfall extremes using a spatially constrained regionalization method

Gao

Carbone

Guo

2015

Intl Journal of Climatology

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Capturing the intensity and return period of extreme rainfall events in the historic record and projecting them into the future are essential to managing, planning, and designing infrastructure. In this study, we assess the performance of the combination of four General Circulation Models (GCMs) and six Regional Climate Models (RCMs) that comprise the North American Regional Climate Change Assessment Program (NARCCAP) and evaluate their performance in simulating rainfall extremes in the continental United States. We adopt a regionalization method to objectively delineate 12 regions in the continental United States with relatively homogenous annual maximum 24‐h rainfall patterns from the North American Regional Reanalysis (NARR) data set. We then compare the Intensity–Duration–Frequency (IDF) curves generated from control simulations of NARCCAP models with those from NARR in each of these regions. We find significant spatial variability of model performance. The models perform reasonably well in many parts of the country, but poorly in the southeastern United States. The GCM providing boundary conditions strongly influences results – output from those RCMs driven by the Community Climate System Model (CCSM) and Canadian Global Climate Model version 3 (CGCM3) matched the NARR data best. Performance of individual RCMs also varied, often in response to nudging, wherein the regional model is constrained by the GCM fields. We also measure changes in bias‐corrected IDF curves generated from NARCCAP projections of the future. In most regions, most models project intensified 24‐h rainfall events in the future (exceptions include some model‐projected decreases in southern California, the extreme north‐central US, Florida, and the Texas Plains). This study provides a valuable means of assessing NARCCAP models' performance in simulating rainfall extremes at the regional scale and understanding how the GCMs, RCMs, and spatial variability affect model performance.

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The Structure of the Real Line

Cited by 35 publications

References 0 publications

On Ohta–Sakai's properties of a topological space

On Ohta–Sakai's properties of a topological space

Banach Spaces of Universal Taylor Series in the Disc Algebra

Assessment of NARCCAP model in simulating rainfall extremes using a spatially constrained regionalization method

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