如何防止.NET的XmlDocument输出中的空白xmlns属性？

var settings = new XmlWriterSettings
{
    OmitXmlDeclaration = true,
    Indent = true,
    NewLineOnAttributes = true
};

using (var writer = XmlWriter.Create("output.xml", settings))
{
    writer.WriteStartElement("root");
    writer.WriteAttributeString("xmlns", "http://www.w3.org/2000/xmlns/");
    writer.WriteElementString("child", "value");
    writer.WriteEndElement();
}

var xns = XNamespace.Get("http://www.w3.org/2000/xmlns/");
var doc = new XElement(xns + "root",
    new XAttribute(XNamespace.None + "xmlns", "http://www.w3.org/2000/xmlns/"),
    new XElement("child", "value")
);

doc.Save("output.xml");

[XmlRoot(Namespace = "http://www.w3.org/2000/xmlns/")]
public class Root
{
    public string Child { get; set; }
}

var root = new Root { Child = "value" };

var serializer = new XmlSerializer(typeof(Root));
var namespaces = new XmlSerializerNamespaces();
namespaces.Add(string.Empty, "http://www.w3.org/2000/xmlns/");

using (var writer = new StreamWriter("output.xml"))
{
    serializer.Serialize(writer, root, namespaces);
}