Estoy desarrollando una aplicación basada en gmap.

Para eso estoy siguiendoesta documento.

Me está dando un error en mainactivity.xml para el siguiente código:

<?xml version="1.0" encoding="utf-8"?>

<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:paddingBottom="@dimen/activity_vertical_margin"
    android:paddingLeft="@dimen/activity_horizontal_margin"
    android:paddingRight="@dimen/activity_horizontal_margin"
    android:paddingTop="@dimen/activity_vertical_margin"
    tools:context=".MainActivity" >


<fragment xmlns:android="http://schemas.android.com/apk/res/android"
          android:id="@+id/map"
          android:layout_width="match_parent"
          android:layout_height="match_parent"
          android:name="com.google.android.gms.maps.MapFragment"/>

</RelativeLayout>

Línea de error:

<fragment xmlns:android="http://schemas.android.com/apk/res/android"

y

<?xml version="1.0" encoding="utf-8"?>

Texto de error:

Description Resource    Path    Location    Type
Unexpected namespace prefix "xmlns" found for tag fragment  activity_main.xml   /gmapAPP/res/layout line 14 Android Lint Problem
The processing instruction target matching "[xX][mM][lL]" is not allowed.   activity_main.xml   /gmapAPP/res/layout line 1  Android XML Format Problem

Mi archivo de manifiesto:

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="com.example.gmapapp"
    android:versionCode="1"
    android:versionName="1.0" >

    <uses-permission android:name="android.permission.INTERNET"/>
    <uses-sdk
        android:minSdkVersion="8"
        android:targetSdkVersion="17" />


    <uses-permission android:name="com.vogella.android.locationapi.maps.permission.MAPS_RECEIVE" />
    <uses-permission android:name="android.permission.INTERNET" />
    <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />
    <uses-permission android:name="com.google.android.providers.gsf.permission.READ_GSERVICES" />
    <uses-permission android:name="android.permission.ACCESS_COARSE_LOCATION" />
    <uses-permission android:name="android.permission.ACCESS_FINE_LOCATION" />

    <application
        android:allowBackup="true"
        android:icon="@drawable/ic_launcher"
        android:label="@string/app_name"
        android:theme="@style/AppTheme" >

        <uses-library android:name="com.google.android.maps"/>

        <activity
            android:name="com.example.gmapapp.MainActivity"
            android:label="@string/app_name" >
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />

                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>

        <meta-data
            android:name="com.google.android.maps.v2.API_KEY"
            android:value="your_apikey" />

    </application>

</manifest>

Por favor, ayúdame.