An area near, but not through, a small burner is cracked - must I replace the cooktop?

actually that's a valid concern as i am too. I do know some of these have breather holes but that's a crack your talking about not a seem or a hole.. I would not use it i would get it replaced or call the manufacturer to understand if its part of their design.. very unlikely.

see this steps and fix it. God bless yo
Relight an oven pilot:

1. Turn all controls off, open the doors, and allow gas to dissipate.
2. Hold a lighted match near the tip of the pilot on the burner assembly. If a burner does not light within two minutes, adjust the pilot, step 3.
3. Turn the pilot adjustment screw (located near the pilot or the thermostat) in small increments and retest until the pilot has a blue flame.
4. Check and replace an oven spark igniter:
   
5. Turn all of the appliance controls off.
6. Open the door and remove the oven bottom and the baffle (see above).
7. Unscrew the igniter from its mounting bracket and inspect it for cracks or other defects. Replace it if it is damaged.
8. To replace a faulty igniter, find the ignition control module, unscrew the cover, and disconnect the module. Install the replacement part and test.

you do not need to replace the whole burner base you need to replace de ignitor

Hello, thank you for your post. It sound like your saying the burners are not lighting up. Most of the time this is just a simple fix. Next time you turn on your burner notice were the igniter sparks this part of the burner needed to be cleaned. You should be able to take the burner cap off and the burner use a wire brush to clean the surface area so the spark has good contact. Take notice also of the igniter you will need to change it out if you see any cracks around the ceramic housing.
Happy Holidays! Please rate me "4 thumbs" if this information was useful.

you need to check the wiring to that burner it appears that there has been a short to the burner

use vaccium,put the vaccium in area were the gas came out or in injectors to **** some of dirt.

A small crack, turns into a big crack, Short of ordering a new piece of glass, there is no "fix" sorry. YOu can continue to use it, but eventually it will run across the cook top, and then shatter the glass... Better be safe than sorry.

Glass on cooktops are not fixable - due to the chance of electrical shocks the manufacturer strongly suggest replacement of the glass.

This is for the glass top units. well i'm not sure if your problem is with your large or small single burner or the large expandable burner. If it's the large or small single burner replace the burner and if it the expandable also replace the burner. If you have a coil burner replace the infinite switch. Good luck hope this helps you.

I not know of any means of repairing same (maybe the system used to fuse auto glass) but if you want to replace it try repairclinic.com Item 935927 or 948440 $216/$227