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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

4 votes
Accepted

Closure of singular points

If I understand correctly, you ask what can be the results of the collision of two singular points, of $A_4$ and $A_1$ types. In general there does not seem to exist an ultimate effective method to tr …
Dmitry Kerner's user avatar
4 votes
0 answers
870 views

A strong form of implicit function theorem (what happens when the derivative is degenerate?)

(this can be considered as some ad) Consider the system of equations $F(x,y)=0$. (Here $x$, $y$ are multi-variables. The equations are over a local ring. e.g. polynomial/analytic/formal/$C^\infty$ et …
Dmitry Kerner's user avatar