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From: "Kyoko Yoshida" <kyokoyoshida123@gmail.com>
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ご回答誠に有難うございます。

>>> で, 「 y は x = x_0 にて連続」の定義は何ですか.
>> For∀ε>0,∃δ>0;|x-x_0|<δ⇒
>> {|y_0-y|∈R;y∈{y∈C;a_m(x)y^m+a_{m-1}(x)y^{m-1}+ …
>> +a_1(x)y+a_0(x)=0},y_0∈{y∈C;a_m(x_0)y^m+a_{m-1}(x_0)y^{m-1}+ …
>> +a_1(x_0)y+a_0(x_0)=0}}⊂[0,ε)
>> だと思います。
> E(x, x_0) = { |y_0 - y| | h(x_0, y_0) = 0, h(x, y) = 0 }
> を考えているのなら, h(x, y) = y^2 - 1 であっても,
> E(x, x_0) = {0, 2} となるので, 連続ではないことになりますね.

すみません。では連続の定義はどうなるのでしょうか?