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Questions tagged [generalized-topology]

A generalized topology, $\mu$ on a set $X$ is a collection of subsets of $X$ s.t. $\varphi\in\mu$ and arbitrary unions of members of $\mu$ belong to $\mu$; and the ordered pair $(X, \mu)$ then stands for a generalized topological space.

A generalized topology (GT, for short) $\mu$ on a set $X$ is a collection of subsets of $X$ such that $\varphi\in\mu$ and arbitrary unions of members of $\mu$ belong to $\mu$; and the ordered pair $(X,\mu)$ then stands for a generalized topological space (abbreviated as GTS).

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On Surfaces of Revolution With Any Two Relations in $\Bbb R^2$ Such that One is the Axis (g) and the Other Revolves (f) defined by z=Rev[f(x),g(x)]:

For the last few years, I have tried a couple times to solve this problem that I came up with. Even though this may seem like a nonsensical idea, there is still a seed of wonder embedded into it. This problem is the one about having one “functional…
Тyma Gaidash
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Some examples of non-spatial frames.

I'm looking for some examples of non-spatial frames. (a frame is non-spatial iff not isomorphic to any frames have forms of topologies for some sets) A simpler example is better for me.
Sho Banno
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Frame morphisms.

The following is a well known fact: A frame morphism $\Phi : B \to A$, considered as a map of posets has a right adjoint $\Psi : A \to B$. My question is, under which hypotesis $\Phi \Psi \Phi = \Phi $ or $\Psi \Phi \Psi = \Psi$? I am asking…
Ivan Di Liberti
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What does the $0$ in "Hodge number is the dimension of $H^{0}(V,\Omega^{n})$" mean please?

Here is the page I was reading.. I tried reading more into what Hodge numbers are and it was too complex for the short amount of time I had but I figured the $0$ probably indicated something like a "(p,q)-forms" where $p=n$ and $q=0$; because it is…
rawiga golf club skateboarder
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How exactly a crosscap relates to a Mobius strip, $^2$, and Klein bottle

Question 1: How exactly a crosscap relates to a Mobius strip, a $^2$, and a Klein bottle? I knew that (1) Mobius strip glued the boundary with a disk $D^2$ is $^2$. (2) Gluing the boundaries of two Mobius strip gives a Klein bottle (3) Connecting…
annie marie cœur
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Is there “information theory” for topological space?

Dear stackexchangicians, I have been reading an expository paper about the information theory founded by C. Shannon. The following question is vague, but has been there successful applications of information theory to study of sets and topological…
Phoenix13
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Monotonicity of semi closure of sets in generalized topological spaces

Hi I just want to ask if anybody here can show that if A is a subset of B then the semi closure of A is a subset of the semi closure of B. I know it is true for closure but I want to be sure if it holds for semi closure as well
user402701
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Union of semi open sets in generalized topological space

In order to define the semi closure of a set in a generalized topological space one must show first that the union of semi open sets is open. I found articles that cite Csaszar but they did not show how he proved it or what his remarks were. Does…
user402701
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Let B be the family of all intervals of the form [a,b).

Then B is the basis for a half-open topology denoted by T" in R. Show that (R,T") is first countable but not second countable. How can I prove it ?
user331899
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Proving [a,b) is first countable but not second countable

Since this half-open interval is neither open nor closed, I have a problem with proving the theorem. Can I have an answer ?
user331899
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Obtaining Generalized Topology by constructing Generalized neighbourhood

$X$ is a given set . To define Generalized Neighborhoods on $X$ Consider $ P ( P (X))$ - the power set of the power set of $X.$ Let $$\psi : X \rightarrow P(P(X))$$ satisfying $x\in V$ for $V\in \psi(x)$. Then $V\in \psi(x)$ is called a …
user118494
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