The question does not seem to make any sense, and this is not about possibility or lack of possibility. The term Ajax is related to Javascript and nothing else:
http://en.wikipedia.org/wiki/Ajax[
^].
The question would make some sense if you somehow hosted some Javascript interpreter and runtime system in your
System.Windows.Forms application, but it's hard to believe: if you worked at that level of sophistication, it would be apparent for you that you could use everything Javascript offers, including Ajax, so you would not ask such a question.
Rather, I suspect that you need to send an HTTP request to some site or Web service and receive HTTP response. But this can be done using the class
System.Net.HttpWebRequest:
http://msdn.microsoft.com/en-us/library/system.net.httpwebrequest%28v=vs.110%29.aspx[
^],
http://msdn.microsoft.com/en-us/library/system.net.webrequest(v=vs.110).aspx[
^].
And of course this is totally unrelated to
System.Windows.Forms or any other UI framework/library or any particular application type.
—SA
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