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Btw.: The historical side of the issue I would like to discuss here

Btw.: The historical side of the issue I would like to discuss here. See for details the marked "Remark" part there motivating essentially why I relate ZCT here with Ehresmann lemma.

This raises Two Questions:

So my motivation is to develop better intuition how much "non algebraicness & pure topology" sits in connectedness & irreducibility of varying fibers. The at least for me the cumbersome point is that in most contemporary literature one deduces ZCT - a statement purely about topology - as consequence of intrinsically algebraic Zariski's Main Theorem resp. prorties of maps of Stein decomposition. And I'm wondering if this statement - which is purely about topology - cannot be deduced with "almost" pure topological methods.

The historical side of the issue I would like to discuss here

Btw.: The historical side of the issue I would like to discuss here

This raises Two Questions:

So my motivation is to develop better intuition how much "non algebraicness & pure topology" sits in connectedness & irreducibility of varying fibers. The at least for me the cumbersome point is that in most contemporary literature one deduces ZCT - a statement purely about topology - as consequence of intrinsically algebraic Zariski's Main Theorem resp. prorties of maps of Stein decomposition. And I'm wondering if this statement - which is purely about topology - cannot be deduced with "almost" pure topological methods.

The historical side of the issue I would like to discuss here