Is this a good plant/weed
I have this ground cover in my yard and I would like to grow it in certain areas as a border. I would like to know if 1) it is considered invasive (I did not see it on the invasive plant list) 2) what it is called. The little purple flowers are about 5 mm in diameter. The flowers close in overcast weather or night time but opens in the sunshine. They are perennial.
This is a type of Veronica, a.k.a. speedwell, there are many types that can be a challenge to tell apart. If you are sure it is a perennial, it may be Germander speedwell (V.chamaedrys) or Slender speedwell (V.filiiformis). People who are growing lawns may find this weedy, but we see it's attractiveness.
Here is a page from our lawn weeds section: http://extension.umd.edu/hgic/topics/speedwell-veronica
The only type of Veronica listed on the invasives plant list is V. serpyllifolia which is Thymeleaf speedwell, whose leaves do not look like yours.