The basement membrane

Three characteristics, and the third one is the surprising one: this tissue has no blood supply of its own.

Figure to be added

Figure 1.15 — a line drawing of epithelial tissue: a row of cells packed tightly against one another with no gaps, each with its nucleus drawn in, the whole row sitting on a thin layer beneath them labelled as the basement membrane.

The characteristics

The cells belonging to epithelial tissue are situated on a basement membrane.
These cells are tightly packed against one another.
This tissue has no blood supply. It is nourished through the basement membrane.

Tightly packed is the point, not an accident

A lining with gaps in it is not a lining. Epithelium has to stop pressure, friction and micro-organisms getting through, so its cells are pressed against one another with nothing between them. That is the opposite of parenchyma, where the intercellular spaces are listed as a characteristic.

No blood supply does not mean no nourishment

Every living tissue needs feeding. Epithelium simply gets it a different way — by diffusion through the basement membrane, from the connective tissue below. Which is also why an epithelium can only be so thick: beyond a few layers, the cells at the top would be too far from their supply.

A blood vessel running through a lining would defeat it

Put a capillary inside an epithelium and you have made a hole in the barrier. The tissue whose job is to seal a surface cannot also be pierced by the vessels that would feed it. Being avascular is not a limitation of epithelium — it is a condition of it working.