Internet access by transmitting digital data over the wires of a local telephone network is provided by DSL (Digital Subscriber Line).

Explanation:
DSL, or Digital Subscriber Line, is a technology that provides high-speed internet access by using existing telephone lines. It allows simultaneous transmission of digital data and voice signals over the same line, without interfering with each other.

Key Points:
Here are some key points that explain why DSL is the correct answer for providing internet access over the wires of a local telephone network:

1. Utilizes Existing Infrastructure: DSL takes advantage of the existing copper telephone lines that are already installed in most homes and businesses. This eliminates the need for laying new cables or infrastructure, making it a cost-effective solution.

2. Broadband Connection: DSL provides a broadband connection, which means it offers high-speed internet access. The data transmission speeds can range from several megabits per second (Mbps) to tens or even hundreds of Mbps, depending on the type of DSL technology used and the distance from the telephone exchange.

3. Separates Voice and Data Signals: DSL technology allows the separation of voice and data signals, enabling users to use the internet and make phone calls simultaneously without any interference. The voice signals are filtered out, allowing uninterrupted internet access.

4. Different Types of DSL: There are different types of DSL technologies, including ADSL (Asymmetric DSL), VDSL (Very High Bitrate DSL), and VDSL2. These variations offer different speeds and performance levels, catering to different user requirements.

5. Distance Limitations: DSL performance can be affected by the distance between the user's location and the telephone exchange. The signal strength decreases as the distance increases, resulting in a decrease in data transmission speed. However, advancements in DSL technology, such as VDSL and VDSL2, have helped overcome some of these limitations and provide higher speeds even over longer distances.

In conclusion, DSL is the correct answer for internet access over the wires of a local telephone network. It utilizes existing telephone lines, provides high-speed broadband connection, separates voice and data signals, and offers different variations to cater to user requirements.