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How is the closed ordinal space compact hausdorff?

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#general-topology #compactness #well-orders #order-topology
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What is definition of order topology?

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#general-topology #order-topology
2.6k
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Is every linear ordered set normal in its order topology?

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#general-topology #order-theory #separation-axioms #order-topology
127
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Compact and connected LOTS

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#general-topology #order-topology
566
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Munkres order topology difference between definition of simple order using $<$ instead of $\leq$

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#general-topology #order-theory #order-topology
465
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Questions about completely normal spaces.

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#general-topology #separation-axioms #order-topology #sorgenfrey-line
1.3k
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Is $[0,1]^2$ with the dictionary order topology separable? First countable?

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#general-topology #proof-verification #order-topology
249
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Complete ordered space

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#general-topology #complete-spaces #order-topology
679
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Is the Function a Homeomorphism?

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#general-topology #order-topology
89
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A set with a topology and a partial ordering question?

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#general-topology #order-theory #lattice-orders #order-topology
51
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Order topology in $\omega^\alpha + 1$ and dynamical systems

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#general-topology #ordinals #order-topology
206
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In an order topology, are connected sets convex, and are they intervals?

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#general-topology #connectedness #order-topology
52
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About compactness of simply ordered set with least upper bound property (Theorem 27.1 of Munkres)

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#general-topology #compactness #upper-lower-bounds #order-topology
2.7k
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Every order topology is regular (proof check)

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#general-topology #proof-verification #separation-axioms #order-topology
434
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Total order and its order topology

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#real-analysis #general-topology #uniform-spaces #order-topology

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