heizitu no gogo ha, tosyokan ga aite irukoto ga ooi desu.

The の connects 平日 and 午後 and makes 平日の午後 mean weekday afternoons or the afternoon on weekdays.

• 平日 = weekday(s)
• 午後 = afternoon
• 平日の午後 = weekday afternoons

You can think of の here as something like of or as a noun linker:

• 週末の夜 = weekend nights
• 夏の朝 = summer mornings

So 平日の午後は means as for weekday afternoons...

The は marks 平日の午後 as the topic of the sentence.

So the sentence is structured like:

• As for weekday afternoons, ...
• On weekday afternoons, ...

This tells the listener what time frame the statement is about.

In English, we often put this kind of information at the beginning naturally:

• On weekday afternoons, the library is often empty.

In Japanese, は is very commonly used to set that stage.

In 図書館が空いている, the が marks 図書館 as the subject of the clause the library is empty / not crowded.

So:

• 図書館が空いている = the library is empty / the library is not crowded

Then that whole clause gets turned into a noun-like phrase with こと:

• 図書館が空いていること = the fact that the library is empty / times when the library is empty

Using が here is very natural because 図書館が空いている is a clause inside a larger sentence.

Also, the main topic of the whole sentence is already 平日の午後は, so using 図書館は would sound different and shift the focus.

Yes, absolutely. This is very common in Japanese.

In this sentence:

• 平日の午後は = the overall topic
• 図書館が = the subject inside the statement about what often happens

So the structure is roughly:

• As for weekday afternoons,
• it is often the case that the library is empty.

A sentence can have:

• one thing marked as the topic with は
• another thing marked as the subject with が

That is normal Japanese grammar.

Here 空いている means not crowded, empty, or having space.

It comes from the verb 空く（あく）.

Depending on context, 空いている can mean different things:

• a seat is free
• a road is clear
• a store is empty
• someone has free time
• a room is not crowded

In this sentence, because the subject is 図書館, the natural meaning is:

• the library is not crowded
• the library tends to be fairly empty

It does not mean open for business here. For that, Japanese would usually use 開いている.

空いて comes from the verb 空く（あく）.

Its て-form is:

• 空く → 空いて

Then adding いる gives:

• 空いている

This pattern often describes a continuing state.

So:

• 空いている = is empty / is open space-wise / is not crowded

This is a very common verb pattern:

• 閉まる → 閉まっている = is closed
• 混む → 混んでいる = is crowded

Because 空いている describes the resulting state: being empty / not crowded.

Compare:

• 空く = to become empty, to open up, to free up
• 空いている = is empty, is available, is not crowded

For a place like a library, if you want to describe its condition, 空いている is the natural form.

So:

• 図書館が空く would sound more like the library becomes empty
• 図書館が空いている means the library is empty / not crowded

こと turns the whole clause before it into a noun-like idea.

So:

• 図書館が空いている = the library is empty
• 図書館が空いていること = the fact that the library is empty / the situation where the library is empty

This is called nominalization.

Japanese often uses こと when an entire action or situation needs to function like a noun.

In this sentence, こと is needed because 多い works with a noun-like thing:

• ことが多い = there are many cases when ... / often ...

ことが多いです is a very common pattern meaning:

• it often happens that ...
• there are many cases where ...
• more naturally in English, just often ...

So:

• 図書館が空いていることが多いです = It is often the case that the library is empty = The library is often not crowded

This pattern is useful for habits, tendencies, and frequent situations.

Examples:

• 朝ごはんを食べないことが多いです。 = I often do not eat breakfast.
• 週末は家にいることが多いです。 = I am often at home on weekends.

In ことが多い, the が marks こと as the subject of 多い.

Literally:

• the cases/facts are many

So:

• 図書館が空いていることが多い = the instances of the library being empty are many

That sounds awkward in English, but it is a normal Japanese structure.

The first が marks the subject inside the clause:

• 図書館が空いている

The second が marks the noun-like phrase as the subject of 多い:

• ことが多い

This is normal Japanese.

Before こと, verbs usually stay in their plain form:

• 空いていること

You do not say:

• 空いていますこと in normal conversation

Then the sentence ends politely with です:

• 多いです

So the sentence mixes:

• plain form inside the clause
• polite ending at the end

That is standard grammar, not a mistake.

多い is an い-adjective, so its polite non-past form is simply:

• 多いです

Examples:

• 高いです
• 安いです
• 多いです

So:

• ことが多いです = there are many cases / it is often the case

多く is a different form used in other grammar patterns, but not here.

Because 平日の午後は is being used as a topic/time setting, not just a simple time marker.

With broad time expressions like:

• 朝
• 午後
• 週末
• 平日
• 夏

Japanese often does not need に.

Compare:

• 平日の午後は、... = As for weekday afternoons, ...
• 午後、図書館に行きます。 = I go to the library in the afternoon.

A specific time like 3時 often takes に:

• 3時に行きます

But broad expressions often do not.

Here it means weekday afternoons in general.

Japanese nouns usually do not explicitly show singular/plural the way English does. The meaning comes from context.

So:

• 平日の午後は here means on weekday afternoons / weekday afternoons generally

It is not talking about one specific weekday afternoon unless the context makes that clear.

Yes. A natural English translation would be something like:

• The library is often not crowded on weekday afternoons.
• On weekday afternoons, the library is often fairly empty.
• The library tends to be quiet on weekday afternoons.

A more literal version is:

• As for weekday afternoons, there are many cases when the library is empty.

The literal version helps show the grammar, but the natural version sounds better in English.

A good breakdown is:

• 平日の午後は = as for weekday afternoons
• 図書館が = the library
• 空いている = is empty / not crowded
• ことが多いです = that happens often

So the full structure is:

[Time/topic] は、[clause] ことが多いです。

This pattern is very useful. For example:

• 週末は、店が混んでいることが多いです。 = On weekends, stores are often crowded.
• 夜は、道が空いていることが多いです。 = At night, the roads are often clear.

Yes, you can, but the nuance changes.

• 図書館が空いていることが多いです focuses more naturally on the situation that the library is empty
• 図書館は空いていることが多いです makes the library more of a topic or contrast

If you are simply stating a general tendency within the topic 平日の午後, 図書館が is very natural.

So the original sentence sounds smooth and standard.

They are:

• 平日 = へいじつ
• の = の
• 午後 = ごご
• は = written は, pronounced わ
• 図書館 = としょかん
• が = が
• 空いて = あいて
• いる = いる
• こと = こと
• が = が
• 多い = おおい
• です = です

So the whole sentence is read:

へいじつ の ごご は、としょかん が あいて いること が おおい です。