redefinition; multiple initialization

I'm writing a program that includes a secondary form using C++/CLI in Visual Studio 2005. So far, I haven't progressed much due to a pair of redefinition errors that don't make much sense.

Mode.h(12) : error C2374: 'NameManipulator::check' : redefinition; multiple initialization
Mode.h(12) : see declaration of 'NameManipulator::check'
Mode.h(22) : error C2011: 'NameManipulator::Mode' : 'class' type redefinition
Mode.h(22) : see declaration of 'NameManipulator::Mode'

I've only declared each of these once, in just one namespace. One was even pre-generated by the compiler. Is there anything I can do to fix this besides starting from scratch? Any help would be much appreciated. (Code below)

using namespace System;
using namespace System::ComponentModel;
using namespace System::Collections;
using namespace System::Windows::Forms;
using namespace System::Data;
using namespace System::Drawing;

namespace NameManipulator {
int check = 4;
/// <summary>
/// Summary for Mode
///
/// WARNING: If you change the name of this class, you will need to change the
///          'Resource File Name' property for the managed resource compiler tool
///          associated with all .resx files this class depends on.  Otherwise,
///          the designers will not be able to interact properly with localized
///          resources associated with this form.
/// </summary>
public ref class Mode : public System::Windows::Forms::Form
{
public:
    Mode(void)
    {
        InitializeComponent();
        //
        //TODO: Add the constructor code here
        //
    }

protected:
    /// <summary>
    /// Clean up any resources being used.
    /// </summary>
    ~Mode()
    {
        if (components)
        {
            delete components;
        }
    }
public: System::Windows::Forms::RadioButton^  rdoAllCaps;
public: System::Windows::Forms::RadioButton^  rdoAllLow;
public: System::Windows::Forms::RadioButton^  rdoReverse;
public: System::Windows::Forms::RadioButton^  rdoNormal;
private: System::Windows::Forms::Button^  btnOK;
protected: 

private:
    /// <summary>
    /// Required designer variable.
    /// </summary>
    System::ComponentModel::Container ^components;

#pragma region Windows Form Designer generated code
    /// <summary>
    /// Required method for Designer support - do not modify
    /// the contents of this method with the code editor.
    /// </summary>
    void InitializeComponent(void)
    {
        this->rdoAllCaps = (gcnew System::Windows::Forms::RadioButton());
        this->rdoAllLow = (gcnew System::Windows::Forms::RadioButton());
        this->rdoReverse = (gcnew System::Windows::Forms::RadioButton());
        this->rdoNormal = (gcnew System::Windows::Forms::RadioButton());
        this->btnOK = (gcnew System::Windows::Forms::Button());
        this->SuspendLayout();
        // 
        // rdoAllCaps
        // 
        this->rdoAllCaps->AutoSize = true;
        this->rdoAllCaps->Location = System::Drawing::Point(12, 12);
        this->rdoAllCaps->Name = L"rdoAllCaps";
        this->rdoAllCaps->Size = System::Drawing::Size(75, 17);
        this->rdoAllCaps->TabIndex = 0;
        this->rdoAllCaps->Text = L"ALL CAPS";
        this->rdoAllCaps->UseVisualStyleBackColor = true;
        // 
        // rdoAllLow
        // 
        this->rdoAllLow->AutoSize = true;
        this->rdoAllLow->Location = System::Drawing::Point(12, 35);
        this->rdoAllLow->Name = L"rdoAllLow";
        this->rdoAllLow->Size = System::Drawing::Size(63, 17);
        this->rdoAllLow->TabIndex = 1;
        this->rdoAllLow->Text = L"all lower";
        this->rdoAllLow->UseVisualStyleBackColor = true;
        this->rdoAllLow->CheckedChanged += gcnew System::EventHandler(this, &Mode::rdoAllLow_CheckedChanged);
        // 
        // rdoReverse
        // 
        this->rdoReverse->AutoSize = true;
        this->rdoReverse->Location = System::Drawing::Point(12, 58);
        this->rdoReverse->Name = L"rdoReverse";
        this->rdoReverse->Size = System::Drawing::Size(71, 17);
        this->rdoReverse->TabIndex = 2;
        this->rdoReverse->Text = L"rEVERSE";
        this->rdoReverse->UseVisualStyleBackColor = true;
        this->rdoReverse->CheckedChanged += gcnew System::EventHandler(this, &Mode::rdoReverse_CheckedChanged);
        // 
        // rdoNormal
        // 
        this->rdoNormal->AutoSize = true;
        this->rdoNormal->Checked = true;
        this->rdoNormal->Location = System::Drawing::Point(12, 81);
        this->rdoNormal->Name = L"rdoNormal";
        this->rdoNormal->Size = System::Drawing::Size(73, 17);
        this->rdoNormal->TabIndex = 3;
        this->rdoNormal->TabStop = true;
        this->rdoNormal->Text = L"rdoNormal";
        this->rdoNormal->UseVisualStyleBackColor = true;
        // 
        // btnOK
        // 
        this->btnOK->DialogResult = System::Windows::Forms::DialogResult::OK;
        this->btnOK->Location = System::Drawing::Point(32, 106);
        this->btnOK->Name = L"btnOK";
        this->btnOK->Size = System::Drawing::Size(33, 23);
        this->btnOK->TabIndex = 4;
        this->btnOK->Text = L"OK";
        this->btnOK->UseVisualStyleBackColor = true;
        // 
        // Mode
        // 
        this->AutoScaleDimensions = System::Drawing::SizeF(6, 13);
        this->AutoScaleMode = System::Windows::Forms::AutoScaleMode::Font;
        this->ClientSize = System::Drawing::Size(99, 138);
        this->ControlBox = false;
        this->Controls->Add(this->btnOK);
        this->Controls->Add(this->rdoNormal);
        this->Controls->Add(this->rdoReverse);
        this->Controls->Add(this->rdoAllLow);
        this->Controls->Add(this->rdoAllCaps);
        this->FormBorderStyle = System::Windows::Forms::FormBorderStyle::FixedSingle;
        this->Name = L"Mode";
        this->StartPosition = System::Windows::Forms::FormStartPosition::CenterParent;
        this->Text = L"Mode";
        this->Load += gcnew System::EventHandler(this, &Mode::Mode_Load);
        this->ResumeLayout(false);
        this->PerformLayout();

    }
#pragma endregion
private: System::Void rdoReverse_CheckedChanged(System::Object^  sender, System::EventArgs^  e){
             if (rdoReverse->Checked == true)
                 check = 3;
         }
private: System::Void Mode_Load(System::Object^  sender, System::EventArgs^  e) {
         }
private: System::Void rdoAllLow_CheckedChanged(System::Object^  sender, System::EventArgs^  e) {
         }
};
}

Your error is that you define the check variable in the header file:

namespace NameManipulator {
    int check = 4;
    // Error in the line above

Change it to a declaration, as this:

namespace NameManipulator {
    extern int check;

and add the definition in a source file:

int NameManipulator::check = 4;