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indiscrete
indiscrete, a. (ɪndɪˈskriːt) Also 7 indiscreet. [ad. L. indiscrēt-us unseparated, undistinguished: see in-3 and discrete, and cf. the differentiated indiscreet.] † 1. Not distinctly separate or distinguishable from contiguous objects or parts. Obs.1608 Topsell Serpents (1658) 629 The Ammodyte, indis... Oxford English Dictionary
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Indiscrete category
An indiscrete category is a category C in which every hom-set C(X, Y) is a singleton. Any two nonempty indiscrete categories are equivalent to each other. wikipedia.org
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Indiscrete topological space is regular and normal How to show that the indiscrete topological space X (where |X|>1)is regular and normal?
If the topology on $X$ is indiscrete, there are only two cases to consider: $F = \emptyset$ and $F = X$.
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What is the difference between indiscrete metric space and indiscrete topological space? What is the difference between indiscrete metric space and indiscrete topological space? I'm confusing both are same. I have al...
If an indiscrete topological space $X$ is metrizable then $X$ is necessarily a singleton whereas it can be any set without metrizability.
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Indiscrete topology convergence Can somebody tell me why every sequence in X converges to every point of X if we consider the indiscrete topology $\tau=${$\emptyset,X$}?
The definition of convergence in topology spaces is: Let X be a topology space and a sequence given by $(x_1,x_2,x_3,...) \in X^{\mathbb N}$. A point $x \in X$ is called **limit point** of $(x_n)_{\mathbb N}$ if for every open set U $\in X$ which contains x holds: There exists an index $n_0 \in \mat...
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Understanding the set of accumulation points of the indiscrete topology > Let $\tau$ be a indiscrete topology on $X$, such that $|X|\geqslant 2$. $A'=\begin{cases} X, & \mbox{ if }|A|\geqslant 2\\\ \emptyset, & \mbox{...
Now, the indiscrete topology on $X$ is $\tau=\\{\emptyset,X\\}$. Let $A\subset X$ s.t $|A|=1$, i.e, $A=\\{a\\}$ for some $a\in X$. Then since we're working in the indiscrete topology, you have $X\backslash A\subset A'$ as well, hence $A'=X\backslash A$.
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Is $(X,\mathcal T)$ necessarily an indiscrete space? > Let $X$ be an infinite set with $\mathcal T$ a topology on $X$. If $X$ is the only infinite subset of $X$ that is open, is $(X,\mathcal T)$ necessarily an indiscr...
You have the right idea, but in order to make it convincing, you have to produce an actual counterexample. Here’s a simple one: let $X=\Bbb N$, and let $\tau=\big\\{\varnothing,\\{0\\},\Bbb N\\}$. It’s straightforward to verify that $\tau$ really is a topology on $X$, and that $X$ is the only infini...
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If we have two-point indiscrete space $X=\{a,b\}$ & let $A=\{a\}$,then what is the derived set of $A?$ If we have two-point indiscrete space $X=\\{a,b\\}$ & let $A=\\{a\\}$,then what is the derived set of $A?$ **Sour...
The closed sets are $\emptyset$ and $X$, the complements of the open sets. $a \notin A'$ because a neighbourhood of $a$ is $X$ and $X \cap A =\\{a\\}$ does not contain a point of $A$ different from $a$! $b \in A'$ because again the **only** neighbourhood of $b$ is $X$ and $X \cap A= \\{a\\}$ contain...
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Why is indiscrete topology unmetrizable? > For instance, the indiscrete topology for $X$ cannot arise from a metric when $X$ has more than one point. One way to see this is to note that the complement of a one-point s...
What you need to do now is assume there exists a metric $d$, and derive a contradiction. For instance, if $X = \\{a,b\\}$, then there is some distance $D = d(a,b) > 0$. What can you now say about the (open) ball of radius $D$ centered at $a$? In other words, which points $x\in X$ satisfy $d(a,x) < D...
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$X$ has Indiscrete topology $\implies$ any subset of $X$ is connected My attempt: Take any $C \subseteq X$. We show $C$ is connected. Suppose $C = A \cup B$ where $A$ and $B$ are disjoint, nonempty subsets (Open $\in ...
You have the basic idea, but you’re missing some crucial pieces. If $C$ is not connected, you can’t guarantee that your $A$ and $B$ are open in $X$; you can only guarantee that they are relatively open in $C$. Thus, you want to show that if $A$ and $B$ are disjoint, relatively open subsets of $C$ su...
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is $(0,1)$ compact in indiscrete topology and discrete topolgy on $\mathbb R$ is $(0,1)$ compact in indiscrete topology and discrete topolgy on $\mathbb R$? i think $(0,1)$ is compact in discrete topology on $\mathb...
As for the indiscrete topology, every set is compact because there is only one possible open cover, namely the space itself.
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Find an example of a topological space with a topology different from the indiscrete topology in which every subset is connected Find an example of a topological space with a topology different from the indiscrete top...
If $A = \\{ a,b \\}$ with topology $\tau = \\{ \varnothing, \\{a\\}, A \\}$, then it is not the indiscrete topology. Isn't this one connected?
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Why set of integer under indiscrete topology is compact? > Why set of integer under indiscrete topology is compact? After looking this question I got surprised as In rudin I read in chapter 2 that compact space is in...
Any set endowed with the indiscrete topology is compact (for lack of infinite open covers), so this says nothing about compactness under different topologies
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Why is every map to an indiscrete space continuous? Show that if $Y$ is a topological space, then every map $f:Y \rightarrow X$ is continuous when $X$ has the indiscrete topology. Proof: Assume $X$ has the indiscret...
Since $X$ has the indiscrete topology, we only have two open subsets. Namely, $X$ and $\varnothing$. Thus, $f$ is continuous regardless to the topology given on $Y$ whenever $X$ is indiscrete.
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Map from indiscrete topological space to usual topological space How can we say that a map from Indiscrete topology on Real numbers to Usual topology on Real numbers is a CONSTANT map?
If $f$ is a function from $\Bbb R$ in the indiscrete topology to $\Bbb R$ in the usual topology then $ f$ is continuous iff it is constant. Any map in the other direction ( so to the indiscrete topology) is always continuous.
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