1,721,264 research outputs found
A note on rank 2 diagonals
Full text link[EN] We solve two questions regarding spaces with a (Gδ)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos about weakly Lindelöf spaces with a Gδ-diagonal of rank 2 and the other is a question of Arhangel’skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.Bella, A.; Spadaro, S. (2020). A note on rank 2 diagonals. Applied General Topology. 21(1):81-85. https://doi.org/10.4995/agt.2020.12065OJS8185211A. V. Arhangel'skii and A. Bella, The diagonal of a first-countable paratopological groups, submetrizability and related results, Appl. Gen. Topol. 8 (2007), 207-212. https://doi.org/10.4995/agt.2007.1881A. V. Arhangel'skii and R. Z. Buzyakova, The rank of the diagonal and submetrizability, Comment. Math. Univ. Carolinae 47 (2006), 585-597.A. Bella, Remarks on the metrizability degree, Boll. Union. Mat. Ital. 1-3 (1987), 391-396.D. Basile, A. Bella and G. J. Ridderbos, Weak extent, submetrizability and diagonal degrees, Houston J. Math. 40 (2014), 255-266.M. Bell, J. Ginsburg and G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79 (1978), no. 1, 37-45. https://doi.org/10.2140/pjm.1978.79.37A. Bella and S. Spadaro, Cardinal invariants of cellular Lindel"of spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), 2805-2811. https://doi.org/10.1007/s13398-019-00660-1R. Buzyakova, Cardinalities of ccc spaces with regular -diagonals, Topology Appl. 153 (2006), 1696-1698. https://doi.org/10.1016/j.topol.2005.06.004J. Chaber, Conditions which imply compactness in countably compact spaces, Bull. Acad. Pol. Sci. Ser. Math. 24 (1976), 993-998.E. K. van Douwen and M. Reed, On chain conditions in Moore spaces II, Topology Appl. 39 (1991), 65-69. https://doi.org/10.1016/0166-8641(91)90076-XJ. Ginsburg and R. G. Woods, A cardinal inequality for topological spaces involving closed discrete sets, Proc. Amer. Math. Soc. 64 (1977), 357-360. https://doi.org/10.1090/S0002-9939-1977-0461407-7J. van Mill, V. V. Tkachuk and R. G. Wilson, Classes defined by stars and neighbourhood assignments, Topology Appl. 154, no. 10 (2007), 2127-2134. https://doi.org/10.1016/j.topol.2006.03.029R. Engelking, General Topology, Heldermann Verlag, Berlin, second ed., 1989.D. Shakhmatov, No upper bound for cardinalities of Tychonoff C.C.C. spaces with a diagonal exist (an answer to J. Ginsburg and R.G. Woods' question), Comment. Math. Univ. Carolinae 25 (1984), 731-746.V. Sneider, Continuous images of Souslin and Borel sets: metrization theorems, Dokl. Acad. Nauk USSR, 50 (1945), 77-79.V. Uspenskij, A large -discrete Fr'echet space having the Souslin property, Comment. Math. Univ. Carolinae 25 (1984), 257-260.W.-F. Xuan and Y.-K. Song, Dually properties and cardinal inequalities, Topology Appl. 234 (2018), 1-6. https://doi.org/10.1016/j.topol.2017.11.002P. Zenor, On spaces with regular -diagonals, Pacific J. Math. 40 (1972), 959-963. https://doi.org/10.2140/pjm.1972.40.75
The role of interleukin-6 in septic patients: why biomarkers cannot substitute our brain
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Upper bounds for the tightness of the Gδ -topology
Full text linkWe prove that if X is a regular space with no uncountable free sequences, then the tightness of its Gδ topology is at most the continuum and if X is, in addition, assumed to be Lindelöf then its Gδ topology contains no free sequences of length larger then the continuum. We also show that, surprisingly, the higher cardinal generalization of our theorem does not hold, by constructing a regular space with no free sequences of length larger than ω1, but whose Gδ topology can have arbitrarily large tightness
A Physiological Point of View on Expiratory (Re)action during Mechanical Ventilation
No full textA commonly held belief about avoiding ventilator-induced lung injury primarily takes into account the inflation half-cycle, whereas deflation is considered to be a passive process about which very little can be done to influence the lung function of patients (1). Is this belief actually correct? We know that patients should be ventilated without harming the lung (so-called rotective lung ventilation) (2). This may be achieved by combining low VT with the correct
amount of positive end-expiratory pressure (PEEP) to minimize the mechanical load on the ventilated lung. However, mechanical ventilation is different from the physiological mechanism that mammals use for gas exchange, in which the inspiratory flow is obtained by the negative pressure generated by the inspiratory muscle. Expiration is often believed to be passive and determined by the elastic recoil pressure of the lung, as it is during physiological ventilation. Unfortunately, expiration is not an exclusively passive phenomenon. The diaphragm not only acts as an inspiratory muscle but also exerts a braking action aimed at slowing down the expiratory flow (3)
A regular non-weakly discretely generated P-space
No full textWe construct a consistent example of a topological space Y= X∪ {∞} such that: (1) Y is regular. (2) Every Gδ subset of Y is open. (3) The point ∞ is not isolated, but it is not in the closure of any discretesubset of X
Electrical impedance tomography: just another tool or a real advance towards precision-medicine in mechanical ventilation?
No full textNo abstract availabl
Can regional lung mechanics evaluation represent the next step towards precision medicine in respiratory care?
No full textOver the last few decades, many randomized clinical trials (RCTs) focused on critically ill patients undergoing mechanical ventilation
have showed negative results.This is true for both RCTs testing different mechanical ventilation strategies or pharmacological interventions. Some authors advocate the heterogeneity in patients’ responses to intervention as one of the main confounding factors leading to negative
RCT. An accurate prediction of individual patient therapeutic responses is necessary to overcome the challenge of patient heterogeneity. In this issue of Minerva Anestesiologica, Zhao et al. investigated the response to a combination of inhaled corticosteroid and β2 agonist on patients undergoing mechanical ventilation due to acute exacerbation of obstructive lung disease or severe asthma. The rationale behind the study was that conventional global lung function could not correctly address the response to therapy due to spatial inhomogeneity. Patients were monitored with the electrical impedance tomography (EIT), a non-invasive monitoring tool which allows a breath-to-breath bedside evaluation of pulmonary ventilation. One of the main advantages given by EIT is the ability to evaluate continuously the mechanical properties of different lung regions, otherwise unrecognizable by global respiratory mechanics
Prone the lung and keep it prone!
No full textProne positioning (PP) has been used for a long time as a rescue therapy for severe hypoxemia in patients with ARDS because of its effectiveness in improving oxygenation and in reducing mortality in those with a more compromised Pao2 to Fio2 ratio (ie, < 150 mm Hg).1 Nevertheless, despite that the clinical indication for PP is to improve gas exchange, its benefits on mortality may be related to its veiled effects on stress and strain distribution, lung concentration of proinflammatory cytokines,2,3 and aeration and ventilation distribution throughout the lung.4,5 To sum up, its potential effects reduce the risk of ventilator-induced lung injury
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