On spaces which are linearly D

AbstractWe introduce a generalization of D-spaces, which we call linearly D-spaces. The following results are obtained for a T1-space X.–X is linearly Lindelöf if, and only if, X is a linearly D-space of countable extent.–X is linearly D provided that X is submetaLindelöf.–X is linearly D provided that X is the union of finitely many linearly D-subspaces.–X is compact provided that X is countably compact and X is the union of countably many linearly D-subspaces

Wijsman Hyperspaces: Subspaces and Embeddings

In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R.Comment: 6 page

On metric spaces with non-equivalent Hewitt and Samuel realcompactifications

Let D be a uniformly discrete space, let \pi be the product uniformity on the countable power D^N of D and let e\pi be the uniformity on D^N induced by all the countable covers in \pi. Assume that the cardinality of D is Ulam measurable. Then (D^N, e\pi) has a Cauchy filterbase, consisting of closed sets, which is not countably centered. As a consequence, the Hewitt and Samuel realcompactifications of (D^N, \pi) are not equivalent.Peer reviewe

Regular Bases At Non-isolated Points And Metrization Theorems

In this paper, we define the spaces with a regular base at non-isolated points and discuss some metrization theorems. We firstly show that a space $X$ is a metrizable space, if and only if $X$ is a regular space with a $\sigma$-locally finite base at non-isolated points, if and only if $X$ is a perfect space with a regular base at non-isolated points, if and only if $X$ is a $\beta$-space with a regular base at non-isolated points. In addition, we also discuss the relations between the spaces with a regular base at non-isolated points and some generalized metrizable spaces. Finally, we give an affirmative answer for a question posed by F. C. Lin and S. Lin in \cite{LL}, which also shows that a space with a regular base at non-isolated points has a point-countable base.Comment: 12 page

On strongly ech-complete spaces

A Tychonoff space X is called strongly ech-complete if there exist paracompact open subsets V1, V2, ... of beta X such that boolean AND(infinity)(n=1) V-n = X. Strong (tech-completeness of a Tychonoff space is characterized in terms of the existence of certain kinds of complete sequence of open covers, for example, of a complete sequence consisting of star-finite open covers. A metrizable space is shown to be strongly (tech-complete if, and only if, the space is (tech-complete and strongly metrizable. Universal spaces for strongly (tech-complete metrizable spaces are indicated. A compatible complete metric is constructed for R such that, for each r > 0, every open r-ball meets at most 25 distinct r-balls. This metric is used to derive characterizations for strongly (tech-complete metrizable spaces and strongly metrizable spaces in terms of special compatible metrics. (C) 2020 Elsevier B.V. All rights reserved.Peer reviewe

Resistenssi : Kasvintuhoojien torjunta-ainekestävyys

Tämä raportti on Suomen oloihin sovellettu katsaus kasvinsuojeluaineiden resistenssin perusteista, esiintymisestä ja ennaltaehkäisemisestä. Raportin aineisto pohjautuu Pohjoismaisen Norbarag (Nordic Baltic Resistance Action Group) -työryhmän 2010-luvulla kokoamiin tietoihin. Kasvintuhoojat (kasvitaudit, tuhoeläimet ja rikkakasvit) haittaavat kasvintuotantoa. Kasvintuhoojien runsautta säädellään viljelykasveista kemiallisilla kasvinsuojeluaineilla eli pestisideillä. Kasvintuhoojapopulaatioon voi syntyä tai siinä voi olla luontaisesti kyky kestää pestisidiä. Tämä kestävyys eli resistenssi on perinnöllistä. Torjunta-aineita tulisi käyttää niin, ettei torjunta-aineresistenssiä synny tai ettei se lisäänny.201

PMEA implies proposition P

AbstractThe Product Measure Extension Axiom (PMEA) asserts that for every set A, Haar measure on 2A can be extended to all subsets of 2A. PMEA implies the normal Moore space conjecture. Proposition P is the statement that every point-finite analytic-additive family of subsets of a metrizable space is σ-discretely decomposible. Proposition P is useful in nonseparable Borel theory. We show in this paper that PMEA implies Proposition P

Adjuvant Capecitabine for Early Breast Cancer: 15-Year Overall Survival Results From a Randomized Trial

PURPOSEFew data are available regarding the influence of adjuvant capecitabine on long-term survival of patients with early breast cancer.METHODSThe Finland Capecitabine Trial (FinXX) is a randomized, open-label, multicenter trial that evaluates integration of capecitabine to an adjuvant chemotherapy regimen containing a taxane and an anthracycline for the treatment of early breast cancer. Between January 27, 2004, and May 29, 2007, 1,500 patients with axillary node-positive or high-risk node-negative early breast cancer were accrued. The patients were randomly allocated to either TX-CEX, consisting of three cycles of docetaxel (T) plus capecitabine (X) followed by three cycles of cyclophosphamide, epirubicin, and capecitabine (CEX, 753 patients), or to T-CEF, consisting of three cycles of docetaxel followed by three cycles of cyclophosphamide, epirubicin, and fluorouracil (CEF, 747 patients). We performed a protocol-scheduled analysis of overall survival on the basis of approximately 15-year follow-up of the patients.RESULTSThe data collection was locked on December 31, 2020. By this date, the median follow-up time of the patients alive was 15.3 years (interquartile range, 14.5-16.1 years) in the TX-CEX group and 15.4 years (interquartile range, 14.8-16.0 years) in the T-CEF group. Patients assigned to TX-CEX survived longer than those assigned to T-CEF (hazard ratio 0.81; 95% CI, 0.66 to 0.99; P = .037). The 15-year survival rate was 77.6% in the TX-CEX group and 73.3% in the T-CEF group. In exploratory subgroup analyses, patients with estrogen receptor–negative cancer and those with triple-negative cancer treated with TX-CEX tended to live longer than those treated with T-CEF.CONCLUSIONAddition of capecitabine to a chemotherapy regimen that contained docetaxel, epirubicin, and cyclophosphamide prolonged the survival of patients with early breast cancer.</p