What is the test for a motion to appeal a judgment against a defendant who failed to provide a timely notice of appeal?

Immediately after entry of judgment, defendant moved in respondent small claims court for leave to appeal therefrom without being required to file the undertaking prescribed by law on the ground that this requirement would unconstitutionally deprive her of property before she could obtain a due process hearing with right to representation by counsel. The motion was denied. Defendant then filed in respondent small claims court a timely notice of appeal but did not accompany that notice with the undertaking required by statute. The appeal was dismissed. Defendant thereupon filed the instant petition. We issued an alternative writ of mandate. By so doing, 'we have necessarily determined that there is no adequate remedy in the ordinary course of law and that (this) case is a proper one for the exercise of our original jurisdiction.' (Westbrook v. Mihaly (1970) 2 Cal.3d 765, 773, 87 Cal.Rptr. 839, 844, 471 P.2d 487, 492, vacated on other grounds (1971) 403 U.S. 915, 91 S.Ct. 2224, 29 L.Ed.2d 692; see County of Sacramento v. Hickman (1967) 66 Cal.2d 841, 845, 59 Cal.Rptr. 609, 428 P.2d 593; Cal. Rules of Court, rule 56(a).)