Function space topologies between the uniform topology and the Whitney topology

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topologizing homeomorphism groups

This paper surveys topologies, called admissible group topologies, of the full group of self-homeomorphisms of a Tychonoff space , which yield continuity of both the group operations and at the same time provide continuity of the evaluation function or, in other words, make the evaluation function a group action of on . By means of a compact extension procedure, beyond local compactness and in two essentially different cases of rim-compactness, we show that the complete upper-semilattice of all admissible group topologies on admits a least element, that can be described simply as a set-open topology and contemporaneously as a uniform topology. But, then, carrying on another efficient way to produce admissible group topologies in substitution of, or in parallel with, the compact extension procedure, we show that rim-compactness is not a necessary condition for the existence of the least admissible group topology. Finally, we give necessary and sufficient conditions for the topology of uniform convergence on the bounded sets of a local proximity space to be an admissible group topology. Also, we cite that local compactness of is not a necessary condition for the compact-open topology to be an admissible group topology of

Proximal convergence

Suppose X is a topological space and Y a proximity space , fn L C f (Leader Convergence) iff for each A in X, B in Y, f(A) near B implies eventually fn (A) is near B. L.C. is a generalization of U. C. (Uniform Convergence). In this paper we study L. C. and various generalizations and prove analogues of the classical results of Arzelà, Dini and others

Risk factors for endocrine complications in transfusion-dependent thalassemia patients on chelation therapy with deferasirox: a risk assessment study from a multicentre nation-wide cohort

Transfusion-dependent patients typically develop iron-induced cardiomyopathy, liver disease, and endocrine complications. We aimed to estimate the incidence of endocrine disorders in transfusion-dependent thalassemia (TDT) patients during long-term iron-chelation therapy with deferasirox (DFX).We developed a multicentre follow-up study of 426 TDT patients treated with once-daily DFX for a median duration of 8 years, up to 18.5 years. At baseline, 118, 121, and 187 patients had 0, 1, or ≥2 endocrine diseases respectively. 104 additional endocrine diseases were developed during the follow-up. The overall risk of developing a new endocrine complication within 5 years was 9.7% (95%CI=6.3-13.1). Multiple Cox regression analysis identified 3 key predictors: age showed a positive log-linear effect (adjusted HR for 50% increase=1.2, 95%CI=1.1-1.3, P=0.005), the serum concentration of thyrotropin (TSH) showed a positive linear effect (adjusted HR for 1 mIU/L increase=1.3, 95%CI=1.1-1.4, P

Disease-specific and general health-related quality of life in newly diagnosed prostate cancer patients: The Pros-IT CNR study

Background: The National Research Council (CNR) prostate cancer monitoring project in Italy (Pros-IT CNR) is an observational, prospective, ongoing, multicentre study aiming to monitor a sample of Italian males diagnosed as new cases of prostate cancer. The present study aims to present data on the quality of life at time prostate cancer is diagnosed. Methods: One thousand seven hundred five patients were enrolled. Quality of life is evaluated at the time cancer was diagnosed and at subsequent assessments via the Italian version of the University of California Los Angeles-Prostate Cancer Index (UCLA-PCI) and the Short Form Health Survey (SF-12). Results: At diagnosis, lower scores on the physical component of the SF-12 were associated to older ages, obesity and the presence of 3+ moderate/severe comorbidities. Lower scores on the mental component were associated to younger ages, the presence of 3+ moderate/severe comorbidities and a T-score higher than one. Urinary and bowel functions according to UCLA-PCI were generally good. Almost 5% of the sample reported using at least one safety pad daily to control urinary loss; less than 3% reported moderate/severe problems attributable to bowel functions, and sexual function was a moderate/severe problem for 26.7%. Diabetes, 3+ moderate/severe comorbidities, T2 or T3-T4 categories and a Gleason score of eight or more were significantly associated with lower sexual function scores at diagnosis. Conclusions: Data collected by the Pros-IT CNR study have clarified the baseline status of newly diagnosed prostate cancer patients. A comprehensive assessment of quality of life will allow to objectively evaluate outcomes of different profile of care