Questions tagged [general-topology]

Everything involving general topological spaces: generation and description of topologies; open and closed sets, neighborhoods; interior, closure; connectedness; compactness; separation axioms; bases; convergence: sequences, nets and filters; continuous functions; compactifications; function spaces; etc. Please use the more specific tags, (algebraic-topology), (differential-topology), (metric-spaces), (functional-analysis) whenever appropriate.

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Can an increasing function be decomposed as a composition of a continuous and discontinuous increasing function

Let $A$ and $B$ be two ordered vector space equipped with the order topology. Let $f:A\to B$ be an increasing function (if $x\leq_A y$ then $f(x)\leq_B f(y)$). Is there two increasing functions $g:A\...