阻止读取时，如何关闭golang os.File？

I start two goroutines to forward message between two io.ReadWriter where rw1 is a TCP connection with type Conn.net and rw2 is the type of *os.File which use pty library to build telnet connection. Here comes the forwarding code:

func Connection(northConn net.Conn) {
    // code omit ...        

    transport(northConn, sourthConn)

    // code omit ...

    sourthConn.Close() // close
}

func transport(rw1, rw2 io.ReadWriter) error {
    errc := make(chan error, 1)
    go func() {
        _, err := io.Copy(rw1, rw2)
        errc <- err
    }()

    go func() {
        _, err := io.Copy(rw2, rw1)
        errc <- err
    }()

    err := <-errc
    if err != nil && err == io.EOF {
        err = nil
    }
    return err
}

The pipeline is "A<->rw1(northConn)<->rw2(sourthConn)<->telnet server" where A communicate with rw1 through TCP connection, rw2 communicate with telnet server through *os.File read and write. The above two goroutines just forwarding message between rw1 and rw2.
These two goroutines can be normally closed if sending exit command from A so that connection between rw2 and telnet server close firstly and A<->rw1 close secondly. But if I shutdown the A terminal which means sending EOF to rw1 only, the A<->rw1 connection can be closed while rw2<->telnet server not. The second goroutine can exit normally while the first goroutine is still blocking at io.Copy(rw1, rw2). And the sourthConn.Close() is blocking too.
So my question is how to make the first goroutine exit in this situation and the sourth.Close() run unblocking? I came up with an idea that send exit command in the second goroutine after rw1 receive EOF but I don't know whether this is a good method and whether this may bring bugs:

go func() {
    _, err := io.Copy(rw2, rw1)
    rw2.Write([]byte("exit
")) // add this sentence
    errc <- err
}()

How can I shutdown the *os.File directly from outside?