Convert download manager to FilePath.

base/file_path.h

 // Copyright (c) 2008 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 // FilePath is a container for pathnames stored in a platform's native string
 // type, providing containers for manipulation in according with the
 // platform's conventions for pathnames.  It supports the following path
 // types:
 //
 //                   POSIX            Windows
@@ skipping 111 matching lines @@
     return path_ == that.path_;
   }
 
   // Required for some STL containers and operations
   bool operator<(const FilePath& that) const {
     return path_ < that.path_;
   }
 
   const StringType& value() const { return path_; }
 
+  bool empty() const { return path_.empty(); }
+
   // Returns true if |character| is in kSeparators.
   static bool IsSeparator(CharType character);
 
   // Returns a FilePath corresponding to the directory containing the path
   // named by this object, stripping away the file component.  If this object
   // only contains one component, returns a FilePath identifying
   // kCurrentDirectory.  If this object already refers to the root directory,
   // returns a FilePath identifying the root directory.
   FilePath DirName() const;
 
@@ skipping 75 matching lines @@
 namespace stdext {
 
 inline size_t hash_value(const FilePath& f) {
   return hash_value(f.value());
 }
 
 }  // namespace stdext
 #endif  // COMPILER
 
 #endif  // BASE_FILE_PATH_H_